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[[Image:Spacings.svg|thumb|right|260px|The maximum spacing method tries to find a distribution function such that the spacings, ''D''<sub>(''i'')</sub>, are all approximately of the same length. This is done by maximizing their [[geometric mean]].]]
 
In [[statistics]], '''maximum spacing estimation''' ('''MSE''' or '''MSP'''), or '''maximum product of spacing estimation (MPS)''', is a method for estimating the parameters of a univariate [[parametric model|statistical model]].<ref name="CA83">{{harvtxt|Cheng|Amin|1983}}</ref> The method requires maximization of the [[geometric mean]] of ''spacings'' in the data, which are the differences between the values of the [[cumulative distribution function]] at neighbouring data points.
 
The concept underlying the method is based on the [[probability integral transform]], in that a set of independent random samples derived from any random variable should on average be uniformly distributed with respect to the cumulative distribution function of the random variable. The MPS method chooses the parameter values that make the observed data as uniform as possible, according to a specific quantitative measure of uniformity.
 
One of the most common methods for estimating the parameters of a distribution from data, the method of [[maximum likelihood]] (MLE), can break down in various cases, such as involving certain mixtures of continuous distributions.<ref name = "R84">{{harvtxt|Ranneby|1984}}</ref> In these cases the method of maximum spacing estimation may be successful.
 
Apart from its use in pure mathematics and statistics, the trial applications of the method have been reported using data from fields such as [[hydrology]],<ref>{{harvtxt|Hall|al.|2004}}</ref> [[econometrics]],<ref>{{harvtxt|Anatolyev|Kosenok|2004}}</ref> and others.<ref>{{harvtxt|Wong|Li|2006}}</ref>
 
==History and usage==
The MSE method was derived independently by Russel Cheng and Nik Amin at the [[Cardiff University|University of Wales Institute of Science and Technology]], and Bo Ranneby at the [[Swedish University of Agricultural Sciences]].<ref name = "R84" /> The authors explained that due to the [[probability integral transform]] at the true parameter, the “spacing” between each observation should be uniformly distributed. This would imply that the difference between the values of the [[cumulative distribution function]] at consecutive observations should be equal. This is the case that maximizes the [[geometric mean]] of such spacings, so solving for the parameters that maximize the geometric mean would achieve the “best” fit as defined this way. {{harvtxt|Ranneby|1984}} justified the method by demonstrating that it is an estimator of the [[Kullback–Leibler divergence]], similar to [[maximum likelihood estimation]], but with more robust properties for various classes of problems.
 
There are certain distributions, especially those with three or more parameters, whose [[Likelihood#Likelihoods for continuous distributions|likelihoods]] may become infinite along certain paths in the [[parameter space]]. Using maximum likelihood to estimate these parameters often breaks down, with one parameter tending to the specific value that causes the likelihood to be infinite, rendering the other parameters inconsistent. The method of maximum spacings, however, being dependent on the difference between points on the cumulative distribution function and not individual likelihood points, does not have this issue, and will return valid results over a much wider array of distributions.<ref name = "CA83" />
 
The distributions that tend to have likelihood issues are often those used to model physical phenomena. {{harvtxt|Hall|al.|2004}} seek to analyze flood alleviation methods, which requires accurate models of river flood effects. The distributions that better model these effects are all three-parameter models, which suffer from the infinite likelihood issue described above, leading to Hall’s investigation of the maximum spacing procedure. {{harvtxt|Wong|Li|2006}}, when comparing the method to maximum likelihood, use various data sets ranging from a set on the oldest ages at death in Sweden between 1905 and 1958 to a set containing annual maximum wind speeds.
 
==Definition==
Given an [[iid]] [[random sample]] {''x''<sub>1</sub>, …, ''x''<sub>''n''</sub>} of size ''n'' from a [[univariate distribution]] with the cumulative distribution function ''F''(''x'';''θ''<sub>0</sub>), where ''θ''<sub>0</sub> ∈ Θ is an unknown parameter to be [[estimation|estimated]], let {''x''<sub>(1)</sub>, …, ''x''<sub>(''n'')</sub>} be the corresponding [[order statistic|ordered]] sample, that is the result of sorting of all observations from smallest to largest. For convenience also denote ''x''<sub>(0)</sub> = −∞ and ''x''<sub>(''n''+1)</sub> = +∞.
 
Define the ''spacings'' as the “gaps” between the values of the distribution function at adjacent ordered points: <ref group="note">The actual definition is sourced to {{harvtxt|Pyke|1965}}, but without direct access to that paper, sourcing is given to {{harvtxt|Pyke|1972}} which defines the spacings in passing. — ''Editor''.<br/> Pyke (1965) starts with “review of previous results known about spacings”, which implies that he hasn't invented them. In fact the first work about the spacings he mentions is “Whitworth (1887)”, although no actual reference was given.</ref>
: <math>
    D_i(\theta) = F(x_{(i)};\,\theta) - F(x_{(i-1)};\,\theta), \quad i=1,\ldots,n+1.
  </math>
 
Then the '''maximum spacing estimator''' of ''θ''<sub>0</sub> is defined as a value that maximizes the [[natural logarithm|logarithm]] of the [[geometric mean]] of sample spacings:
: <math>
  \hat{\theta} = \underset{\theta\in\Theta}{\operatorname{arg\,max}} \; S_n(\theta),
  \quad\text{where }\
  S_n(\theta) = \ln\!\! \sqrt[n+1]{D_1D_2\cdots D_{n+1}}
                = \frac{1}{n+1}\sum_{i=1}^{n+1}\ln{D_i}(\theta).
  </math>
 
By the [[inequality of arithmetic and geometric means]], function ''S''<sub>''n''</sub>(''θ'') is bounded from above by −ln(''n''+1), and thus the maximum has to exist at least in the [[supremum]] sense.
 
Note that some authors define the function ''S''<sub>''n''</sub>(''θ'') somewhat differently. In particular, {{harvtxt|Ranneby|1984}} multiplies each ''D''<sub>''i''</sub> by a factor of (''n''+1), whereas {{harvtxt|Cheng|Stephens|1989}} omit the {{frac|''n''+1}} factor in front of the sum and add the “−” sign in order to turn the maximization into minimization. As these are constants with respect to ''θ'', the modifications do not alter the location of the maximum of the function ''S''<sub>''n''</sub>.
 
==Examples==
This section presents two examples of calculating the maximum spacing estimator.
 
===Example 1===
[[Image:Spacing Estimation plot for MSE example.svg|thumb|right|350px|alt=A box containing the graph of two offset concave functions with different peaks, vertical lines bisecting the peaks, and labeled arrows pointing to where the vertical lines intersect the bottom of the box.|Plots of the [[Natural logarithm|log]] value of ''λ'' for the simplistic example under both likelihood and spacing estimation. The values for which both likelihood and spacing are maximized, the maximum likelihood and maximum spacing estimates, are identified.]]
 
Suppose two values ''x''<sub>(1)</sub> = 2, ''x''<sub>(2)</sub> = 4 were sampled from the [[exponential distribution]] ''F''(''x'';''λ'') = 1 − e<sup>−''xλ''</sup>, ''x'' ≥ 0 with unknown parameter ''λ'' > 0. In order to construct the MSE we have to first find the spacings:
<center>
{| class="wikitable"
|-
! ''i'' !! ''F''(''x''<sub>(''i'')</sub>)  !! ''F''(''x''<sub>(''i''−1)</sub>)  !! ''D''<sub>''i''</sub> = ''F''(''x''<sub>(''i'')</sub>) − ''F''(''x''<sub>(''i''−1)</sub>)
|-
|  1  || 1 − e<sup>−2''λ''</sup>  || 0                        || 1 − e<sup>−2''λ''</sup> 
|-
|  2  || 1 − e<sup>−4''λ''</sup>  || 1 − e<sup>−2''λ''</sup>  || e<sup>−2''λ''</sup> − e<sup>−4''λ''</sup> 
|-
|  3  || 1                        || 1 − e<sup>−4''λ''</sup>  || e<sup>−4''λ''</sup> 
|}
</center>
 
The process continues by finding the ''λ'' that maximizes the geometric mean of the “difference” column. Using the convention that ignores taking the (''n''+1)<sup>st</sup> root, this turns into the maximization of the following product: (1 − e<sup>−2''λ''</sup>) · (e<sup>−2''λ''</sup> − e<sup>−4''λ''</sup>) · (e<sup>−4''λ''</sup>). Letting ''μ'' = e<sup>−2''λ''</sup>, the problem becomes finding the maximum of ''μ''<sup>5</sup>−2''μ''<sup>4</sup>+''μ''<sup>3</sup>. Differentiating, the ''μ'' has to satisfy 5''μ''<sup>4</sup>−8''μ''<sup>3</sup>+3''μ''<sup>2</sup> = 0. This equation has roots 0, 0.6, and 1. As ''μ'' is actually e<sup>−2''λ''</sup>, it has to be greater than zero but less than one. Therefore, the only acceptable solution is
: <math>
    \mu=0.6 \quad \Rightarrow \quad \lambda_{\text{MSE}} = \frac{\ln 0.6}{-2} \approx 0.255,
  </math>
which corresponds to an exponential distribution with a mean of {{frac|''λ''}} ≈ 3.915. For comparison, the maximum likelihood estimate of λ is the inverse of the sample mean, 3, so ''λ''<sub>MLE</sub> = ⅓ ≈ 0.333.
 
===Example 2===
Suppose {''x''<sub>(1)</sub>, …, ''x''<sub>(''n'')</sub>} is the ordered sample from a [[Uniform distribution (continuous)|uniform distribution]] ''U''(''a'',''b'') with unknown endpoints ''a'' and ''b''. The cumulative distribution function is ''F''(''x'';''a'',''b'') = (''x''−''a'')/(''b''−''a'') when ''x''∈[''a'',''b'']. Therefore individual spacings are given by
: <math>
    D_1 = \frac{x_{(1)}-a}{b-a}, \ \
    D_i = \frac{x_{(i)}-x_{(i-1)}}{b-a}\ \text{for } i = 2, \ldots, n, \ \
    D_{n+1} = \frac{b-x_{(n)}}{b-a} \ \
  </math>
 
Calculating the geometric mean and then taking the logarithm, statistic ''S''<sub>''n''</sub> will be equal to
: <math>
    S_n(a,b) = \tfrac{1}{n+1}\ln(x_{(1)}-a) + \tfrac{1}{n+1}\ln(b-x_{(n)}) - \ln(b-a) + \sum_{i=2}^n \ln(x_{(i)}-x_{(i-1)})
  </math>
Here only the first three terms depend on the parameters ''a'' and ''b''. Differentiating with respect to those parameters and solving the resulting linear system, the maximum spacing estimates will be
: <math alt="MS estimator of a is the minimal x minus the sample range divided by n−1; MS estimator of b is the maximal x plus the sample range divided by n−1">
    \hat{a} = \frac{nx_{(1)} - x_{(n)}}{n-1},\ \ \hat{b} = \frac{nx_{(n)}-x_{(1)}}{n-1}.
  </math>
These are known to be the [[uniformly minimum variance unbiased]] (UMVU) estimators for the continuous uniform distribution. In comparison, the maximum likelihood estimates for this problem <math alt="ML estimate of a is the smallest of x’s">\scriptstyle\hat{a}=x_{(1)}</math> and <math alt="ML estimate of b is the largest of x’s">\scriptstyle\hat{b}=x_{(n)}</math> are biased and have higher [[mean-squared error]].
 
==Properties==
===Consistency and efficiency===
{{Expand section|date=May 2010}}
{{multiple image
  | width    = 200
  | footer    = Plot of a “J-shaped” density function and its corresponding distribution. A [[Weibull distribution#Related distributions|shifted Weibull]] with a [[scale parameter]] of 15, a [[shape parameter]] of 0.5, and a [[location parameter]] of 10. The density asymptotically approaches infinity as ''x'' approaches 10, rendering the estimates of the other parameters inconsistent. Note that there is no [[inflection point]] in the graph of the distribution.
  | image1    = J-shaped density.svg
  | alt1      = A box containing a graph of an offset straight line and a "reverse J" curve that rises to meet the straight line.
  | caption1  = Density
  | image2    = J-shaped density - corresponding distribution.svg
  | alt2      = A box containing a graph of an offset straight line and a "J" curve that rises from the straight line.
  | caption2  = Distribution
}}
 
The maximum spacing estimator is a [[consistent estimator]] in that it [[convergence in probability|converges in probability]] to the true value of the parameter, ''θ''<sub>0</sub>, as the sample size increases to infinity.<ref name = "R84" /> The consistency of maximum spacing estimation holds under much more general conditions than for [[maximum likelihood]] estimators. In particular, in cases where the underlying distribution is J-shaped, maximum likelihood will fail where MSE succeeds.<ref name = "CA83" /> An example of a J-shaped density is the [[Weibull distribution]], specifically a [[Weibull distribution#Related distributions|shifted Weibull]], with a [[shape parameter]] less than 1. The density will tend to infinity as ''x'' approaches the [[location parameter]] rendering estimates of the other parameters inconsistent.
 
Maximum spacing estimators are also at least as [[Efficiency (statistics)#Asymptotic efficiency|asymptotically efficient]] as maximum likelihood estimators, where the latter exist. However, MSEs may exist in cases where MLEs do not.<ref name = "CA83" />
 
===Sensitivity===
Maximum spacing estimators are sensitive to closely spaced observations, and especially ties.<ref name = "CS89">{{harvtxt|Cheng|Stephens|1989}}</ref> Given
: <math>
    X_{i+k} = X_{i+k-1}=\cdots=X_i, \,
  </math>
we get
: <math>
    D_{i+k}(\theta) = D_{i+k-1}(\theta) = \cdots = D_{i+1}(\theta) = 0. \,
  </math>
 
When the ties are due to multiple observations, the repeated spacings (those that would otherwise be zero) should be replaced by the corresponding likelihood.<ref name = "CA83" /> That is, one should substitute <math>f_{i}(\theta)</math> for <math>D_i(\theta)</math>, as
: <math>
    \lim_{x_i \to x_{i-1}}\frac{\int_{x_{i-1}}^{x_i}f(t;\theta)dt}{(x_i-x_{i-1})} = f(x_{i-1},\theta) = f(x_{i},\theta),
  </math>
since <math>x_{i} = x_{i-1}</math>.
 
When ties are due to rounding error, {{harvtxt|Cheng|Stephens|1989}} suggest another method to remove the effects.<ref group="note">There appear to be some minor typographical errors in the paper. For example, in section 4.2, equation (4.1), the rounding replacement for <math>D_j</math>, should not have the log term. In section 1, equation (1.2), <math>D_j</math> is defined to be the spacing itself, and <math>M(\theta)</math> is the negative sum of the logs of <math>D_j</math>. If <math>D_j</math> is logged at this step, the result is always =<0, as the difference between two adjacent points on a cumulative distribution is always &le; 1, and strictly &lt;1 unless there are only two points at the bookends. Also, in section 4.3, on page 392, calculation shows that it is the variance <math>\textstyle\tilde{\sigma^2}</math> which has MPS estimate of 6.87, not the standard deviation <math>\textstyle\tilde{\sigma}</math>. -- ''Editor''</ref>
Given ''r'' tied observations from ''x''<sub>''i''</sub> to ''x''<sub>''i+r''−1</sub>, let ''δ'' represent the [[round-off error]]. All of the true values should then fall in the range <math>x \pm \delta</math>. The corresponding points on the distribution should now fall between <math>y_L = F(x-\delta, \hat\theta)</math> and <math>y_U = F(x+\delta, \hat\theta)</math>. Cheng and Stephens suggest assuming that the rounded values are [[Uniform distribution (continuous)|uniformly spaced]] in this interval, by defining
: <math>
    D_j = \frac{y_U-y_L}{r-1} \quad (j=i+1,\ldots,i+r-1).
  </math>
 
The MSE method is also sensitive to secondary clustering.<ref name = "CS89" /> One example of this phenomenon is when a set of observations is thought to come from a single [[normal distribution]], but in fact comes from a [[Mixture (probability)|mixture]] normals with different means. A second example is when the data is thought to come from an [[exponential distribution]], but actually comes from a [[gamma distribution]]. In the latter case, smaller spacings may occur in the lower tail. A high value of ''M''(''θ'') would indicate this secondary clustering effect, and suggesting a closer look at the data is required.<ref name = "CS89" />
 
==Goodness of fit==
The statistic ''S<sub>n</sub>''(''θ'') is also a form of [[Pat Moran (statistician)|Moran]] or Moran-Darling statistic, ''M''(''θ''), which can be used to test [[goodness of fit]].<ref group="note">The literature refers to related statistics as Moran or Moran-Darling statistics. For example, {{harvtxt|Cheng|Stephens|1989}} analyze the form <math>\scriptstyle M(\theta)= -\sum_{j=1}^{n+1}\log{D_i(\theta)}</math> where <math>\scriptstyle D_i(\theta)</math> is defined as above. {{harvtxt|Wong|Li|2006}} use the same form as well. However, {{harvtxt|Beirlant|al.|2001}} uses the form <math>\scriptstyle M_n= -\sum_{j=0}^{n}\ln{((n + 1)(X_{n,i+1} - X_{n,i}))}</math>, with the additional factor of <math>(n+1)</math> inside the logged summation. The extra factors will make a difference in terms of the expected mean and variance of the statistic. For consistency, this article will continue to use the Cheng & Amin/Wong & Li form. -- ''Editor''</ref>
It has been shown that the statistic, when defined as
: <math>
    S_n(\theta) = M_n(\theta)= -\sum_{j=1}^{n+1}\ln{D_j(\theta)},
  </math>
is [[Estimator#Asymptotic normality|asymptotically normal]], and that a chi-squared approximation exists for small samples.<ref name = "CS89" /> In the case where we know the true parameter <math>\theta^0</math>, {{harvtxt|Cheng|Stephens|1989}} show that the statistic <math>\scriptstyle M_n(\theta)</math> has a [[normal distribution]] with
: <math>\begin{align}
  \mu_M      & \approx (n+1)(\ln(n+1)+\gamma)-\frac{1}{2}-\frac{1}{12(n+1)},\\
  \sigma^2_M & \approx (n+1)\left ( \frac{\pi^2}{6} -1 \right ) -\frac{1}{2}-\frac{1}{6(n+1)},
  \end{align}</math>
where ''γ'' is the [[Euler–Mascheroni constant]] which is approximately 0.57722.<ref group="note">{{harvtxt|Wong|Li|2006}} leave out the [[Euler–Mascheroni constant]] from their description. -- ''Editor''</ref>
 
The distribution can also be approximated by that of <math>A</math>, where
: <math>
    A = C_1 + C_2\chi^2_n \,
  </math>,
in which
: <math>\begin{align}
    C_1 &= \mu_M - \sqrt{\frac{\sigma^2_Mn}{2}},\\
    C_2 &= {\sqrt\frac{\sigma^2_M}{2n}},\\
  \end{align}</math>
and where <math>\chi^2_n</math> follows a [[chi-squared distribution]] with <math>n</math> [[Degrees of freedom (statistics)|degrees of freedom]]. Therefore, to test the hypothesis <math>H_0</math> that a random sample of <math>n</math> values comes from the distribution <math>F(x,\theta)</math>, the statistic <math>T(\theta)= \frac{M(\theta)-C_1}{C_2}</math> can be calculated. Then <math>H_0</math> should be rejected with [[Statistical significance|significance]] <math>\alpha</math> if the value is greater than the [[critical value]] of the appropriate chi-squared distribution.<ref name = "CS89" />
 
Where ''θ''<sub>0</sub> is being estimated by <math>\hat\theta</math>, {{harvtxt|Cheng|Stephens|1989}} showed that <math>S_n(\hat\theta) = M_n(\hat\theta)</math> has the same asymptotic mean and variance as in the known case. However, the test statistic to be used requires the addition of a bias correction term and is:
: <math>
    T(\hat\theta) =  \frac{M(\hat\theta)+\frac{k}{2}-C_1}{C_2},
  </math>
where <math>k</math> is the number of parameters in the estimate.
 
==Generalized maximum spacing==
===Alternate measures and spacings===
{{harvtxt|Ranneby|Ekström|1997}} generalized the MSE method to approximate other [[F-divergence|measures]] besides the Kullback&ndash;Leibler measure. {{harvtxt|Ekström|1997}} further expanded the method to investigate properties of estimators using higher order spacings, where an ''m''-order spacing would be defined as <math>F(X_{j+m}) - F(X_{j})</math>.
 
===Multivariate distributions===
{{harvtxt|Ranneby|al.|2005}} discuss extended maximum spacing methods to the [[Joint probability distribution|multivariate]] case. As there is no natural order for <math>\mathbb{R}^k (k>1)</math>, they discuss two alternative approaches: a geometric approach based on [[Dirichlet cell]]s and a probabilistic approach based on a “nearest neighbor ball” metric.
 
==See also==
* [[Kullback–Leibler divergence]]
* [[Maximum likelihood]]
* [[Probability distribution]]
 
==Notes==
{{Reflist|group="note"}}
 
==References==
{{Reflist|3}}
 
===Works Cited===
{{refbegin}}
* {{cite journal
| last1 = Anatolyev | first1 = Stanislav
| last2 = Kosenok  | first2 = Grigory
| year  = 2005
| title = An alternative to maximum likelihood based on spacings
| journal = Econometric Theory
| volume = 21 | issue = 2 | pages = 472–476
| doi = 10.1017/S0266466605050255
| url = http://fir.nes.ru/~gkosenok/MPS.pdf
| accessdate = 2009-01-21
| ref = CITEREFAnatolyevKosenok2004
}}
* {{cite journal
| last1 = Beirlant      | first1 = J.
| last2 = Dudewicz      | first2 = E.J.
| last3 = Györfi        | first3 = L.
| last4 = van der Meulen | first4 = E.C.
| year  = 1997
| title = Nonparametric entropy estimation: an overview
| journal = International Journal of Mathematical and Statistical Sciences
| volume = 6 | issue = 1 | pages = 17–40
| issn = 1055-7490
| url = http://www.menem.com/ilya/digital_library/entropy/beirlant_etal_97.pdf
| accessdate = 2008-12-31
| ref = CITEREFBeirlantal.2001
|archiveurl = http://web.archive.org/web/20050505044534/http://www.menem.com/ilya/digital_library/entropy/beirlant_etal_97.pdf |archivedate = May 5, 2005}} <small>''Note: linked paper is an updated 2001 version.''</small>
* {{cite journal
| last1 = Cheng | first1 = R.C.H.
| last2 = Amin  | first2 = N.A.K.
| year  = 1983
| title = Estimating parameters in continuous univariate distributions with a shifted origin
| journal = Journal of the Royal Statistical Society, Series B
| volume = 45 | issue = 3 | pages = 394–403
| issn = 0035-9246
| jstor = 2345411
| ref = harv
}}
* {{cite journal
| last1 = Cheng    | first1 = R.C.H
| last2 = Stephens | first2 = M. A.
| year  = 1989
| title = A goodness-of-fit test using Moran’s statistic with estimated parameters
| journal = Biometrika
| volume = 76 | issue = 2 | pages = 386–392
| doi = 10.1093/biomet/76.2.385
| ref = harv
}}
* {{cite journal
| last  = Ekström
| first = Magnus
| year  = 1997
| title = Generalized maximum spacing estimates
| journal = University of Umeå, Department of Mathematics
| volume = 6
| issn = 0345-3928
| url = http://www.matstat.umu.se/varia/reports/rep9706.ps.gz
| accessdate = 2008-12-30
| ref = harv
|archiveurl = http://web.archive.org/web/20070214143052/http://www.matstat.umu.se/varia/reports/rep9706.ps.gz |archivedate = February 14, 2007}}
* {{cite journal
| last1 = Hall            | first1 = M.J.
| last2 = van den Boogaard | first2 = H.F.P.
| last3 = Fernando        | first3 = R.C.
| last4 = Mynett          | first4 = A.E.
| year  = 2004
| title = The construction of confidence intervals for frequency analysis using resampling techniques
| journal = Hydrology and Earth System Sciences
| volume = 8 | issue = 2 | pages = 235–246
| issn = 1027-5606
| url = http://www.hydrol-earth-syst-sci.net/8/235/2004/hess-8-235-2004.pdf
| accessdate = 2009-01-21
| ref = CITEREFHallal.2004
}}
* {{cite journal
| last  = Pyke | first = Ronald
| year  = 1965
| title = Spacings
| journal = Journal of the Royal Statistical Society, Series B
| volume = 27 | pages = 395–449
| issn = 0035-9246
| jstor = 2345793
| ref = harv
| issue  = 3
}}
* {{cite journal
| last  = Pyke | first = Ronald
| year  = 1972
| title = Spacings revisited
| journal = Proceedings of the sixth Berkeley symposium on mathematical statistics and probability
| volume = 1 | pages = 417–427
| publisher = University of California Press
| issn = 0097-0433
| mr = 0405709
| zbl=0234.62008
| url = http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.bsmsp/1200514103
| accessdate = 2010-03-18
| ref = harv
}}
* {{cite journal
| last  = Ranneby | first = Bo
| year  = 1984
| title = The maximum spacing method. An estimation method related to the maximum likelihood method
| journal = Scandinavian Journal of Statistics
| volume = 11 | issue = 2 | pages = 93–112
| issn = 0303-6898
| jstor = 4615946
| ref = harv
}}
* {{cite journal
| last1 = Ranneby | first1 = Bo
| last2 = Ekström | first2 = Magnus
| year  = 1997
| title = Maximum spacing estimates based on different metrics
| journal = University of Umeå, Department of Mathematics
| volume = 5
| issn = 0345-3928
| url = http://www.matstat.umu.se/varia/reports/rep9705.ps.gz
| accessdate = 2008-12-30
| ref = harv
|archiveurl = http://web.archive.org/web/20070214143042/http://www.matstat.umu.se/varia/reports/rep9705.ps.gz |archivedate = February 14, 2007}}
* {{cite journal
| last1 = Ranneby        | first1 = Bo
| last2 = Jammalamadakab | first2 = S. Rao
| last3 = Teterukovskiy  | first3 = Alex
| year  = 2005
| title = The maximum spacing estimation for multivariate observations
| journal = Journal of Statistical Planning and Inference
| volume = 129 | issue = 1–2 | pages = 427–446
| doi = 10.1016/j.jspi.2004.06.059
| url = http://www.pstat.ucsb.edu/faculty/jammalam/html/research%20publication_files/MSP2.pdf
| accessdate = 2008-12-31
| ref = CITEREFRannebyal.2005
}}
* {{cite book
| last1 = Wong | first1 = T.S.T
| last2 = Li  | first2 = W.K.
| year = 2006
| title = Time series and related topics: in memory of Ching-Zong Wei
| chapter = A note on the estimation of extreme value distributions using maximum product of spacings
| location = Beachwood, Ohio | publisher = Institute of Mathematical Statistic
| pages = 272–283
| doi = 10.1214/074921706000001102
| arxiv = math/0702830v1
| ref = harv
}}
{{refend}}
 
{{Statistics}}
 
{{good article}}
 
{{DEFAULTSORT:Maximum Spacing Estimation}}
[[Category:Estimation theory]]
[[Category:Fitting probability distributions]]

Revision as of 04:28, 20 January 2014

The maximum spacing method tries to find a distribution function such that the spacings, D(i), are all approximately of the same length. This is done by maximizing their geometric mean.

In statistics, maximum spacing estimation (MSE or MSP), or maximum product of spacing estimation (MPS), is a method for estimating the parameters of a univariate statistical model.[1] The method requires maximization of the geometric mean of spacings in the data, which are the differences between the values of the cumulative distribution function at neighbouring data points.

The concept underlying the method is based on the probability integral transform, in that a set of independent random samples derived from any random variable should on average be uniformly distributed with respect to the cumulative distribution function of the random variable. The MPS method chooses the parameter values that make the observed data as uniform as possible, according to a specific quantitative measure of uniformity.

One of the most common methods for estimating the parameters of a distribution from data, the method of maximum likelihood (MLE), can break down in various cases, such as involving certain mixtures of continuous distributions.[2] In these cases the method of maximum spacing estimation may be successful.

Apart from its use in pure mathematics and statistics, the trial applications of the method have been reported using data from fields such as hydrology,[3] econometrics,[4] and others.[5]

History and usage

The MSE method was derived independently by Russel Cheng and Nik Amin at the University of Wales Institute of Science and Technology, and Bo Ranneby at the Swedish University of Agricultural Sciences.[2] The authors explained that due to the probability integral transform at the true parameter, the “spacing” between each observation should be uniformly distributed. This would imply that the difference between the values of the cumulative distribution function at consecutive observations should be equal. This is the case that maximizes the geometric mean of such spacings, so solving for the parameters that maximize the geometric mean would achieve the “best” fit as defined this way. Template:Harvtxt justified the method by demonstrating that it is an estimator of the Kullback–Leibler divergence, similar to maximum likelihood estimation, but with more robust properties for various classes of problems.

There are certain distributions, especially those with three or more parameters, whose likelihoods may become infinite along certain paths in the parameter space. Using maximum likelihood to estimate these parameters often breaks down, with one parameter tending to the specific value that causes the likelihood to be infinite, rendering the other parameters inconsistent. The method of maximum spacings, however, being dependent on the difference between points on the cumulative distribution function and not individual likelihood points, does not have this issue, and will return valid results over a much wider array of distributions.[1]

The distributions that tend to have likelihood issues are often those used to model physical phenomena. Template:Harvtxt seek to analyze flood alleviation methods, which requires accurate models of river flood effects. The distributions that better model these effects are all three-parameter models, which suffer from the infinite likelihood issue described above, leading to Hall’s investigation of the maximum spacing procedure. Template:Harvtxt, when comparing the method to maximum likelihood, use various data sets ranging from a set on the oldest ages at death in Sweden between 1905 and 1958 to a set containing annual maximum wind speeds.

Definition

Given an iid random sample {x1, …, xn} of size n from a univariate distribution with the cumulative distribution function F(x;θ0), where θ0 ∈ Θ is an unknown parameter to be estimated, let {x(1), …, x(n)} be the corresponding ordered sample, that is the result of sorting of all observations from smallest to largest. For convenience also denote x(0) = −∞ and x(n+1) = +∞.

Define the spacings as the “gaps” between the values of the distribution function at adjacent ordered points: [note 1]

Then the maximum spacing estimator of θ0 is defined as a value that maximizes the logarithm of the geometric mean of sample spacings:

By the inequality of arithmetic and geometric means, function Sn(θ) is bounded from above by −ln(n+1), and thus the maximum has to exist at least in the supremum sense.

Note that some authors define the function Sn(θ) somewhat differently. In particular, Template:Harvtxt multiplies each Di by a factor of (n+1), whereas Template:Harvtxt omit the Template:Frac factor in front of the sum and add the “−” sign in order to turn the maximization into minimization. As these are constants with respect to θ, the modifications do not alter the location of the maximum of the function Sn.

Examples

This section presents two examples of calculating the maximum spacing estimator.

Example 1

A box containing the graph of two offset concave functions with different peaks, vertical lines bisecting the peaks, and labeled arrows pointing to where the vertical lines intersect the bottom of the box.
Plots of the log value of λ for the simplistic example under both likelihood and spacing estimation. The values for which both likelihood and spacing are maximized, the maximum likelihood and maximum spacing estimates, are identified.

Suppose two values x(1) = 2, x(2) = 4 were sampled from the exponential distribution F(x;λ) = 1 − e, x ≥ 0 with unknown parameter λ > 0. In order to construct the MSE we have to first find the spacings:

i F(x(i) F(x(i−1) Di = F(x(i)) − F(x(i−1))
 1  1 − e−2λ  0 1 − e−2λ 
 2  1 − e−4λ  1 − e−2λ  e−2λ − e−4λ 
 3  1 1 − e−4λ  e−4λ 

The process continues by finding the λ that maximizes the geometric mean of the “difference” column. Using the convention that ignores taking the (n+1)st root, this turns into the maximization of the following product: (1 − e−2λ) · (e−2λ − e−4λ) · (e−4λ). Letting μ = e−2λ, the problem becomes finding the maximum of μ5−2μ4+μ3. Differentiating, the μ has to satisfy 5μ4−8μ3+3μ2 = 0. This equation has roots 0, 0.6, and 1. As μ is actually e−2λ, it has to be greater than zero but less than one. Therefore, the only acceptable solution is

which corresponds to an exponential distribution with a mean of Template:Frac ≈ 3.915. For comparison, the maximum likelihood estimate of λ is the inverse of the sample mean, 3, so λMLE = ⅓ ≈ 0.333.

Example 2

Suppose {x(1), …, x(n)} is the ordered sample from a uniform distribution U(a,b) with unknown endpoints a and b. The cumulative distribution function is F(x;a,b) = (xa)/(ba) when x∈[a,b]. Therefore individual spacings are given by

Calculating the geometric mean and then taking the logarithm, statistic Sn will be equal to

Here only the first three terms depend on the parameters a and b. Differentiating with respect to those parameters and solving the resulting linear system, the maximum spacing estimates will be

These are known to be the uniformly minimum variance unbiased (UMVU) estimators for the continuous uniform distribution. In comparison, the maximum likelihood estimates for this problem and are biased and have higher mean-squared error.

Properties

Consistency and efficiency

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The maximum spacing estimator is a consistent estimator in that it converges in probability to the true value of the parameter, θ0, as the sample size increases to infinity.[2] The consistency of maximum spacing estimation holds under much more general conditions than for maximum likelihood estimators. In particular, in cases where the underlying distribution is J-shaped, maximum likelihood will fail where MSE succeeds.[1] An example of a J-shaped density is the Weibull distribution, specifically a shifted Weibull, with a shape parameter less than 1. The density will tend to infinity as x approaches the location parameter rendering estimates of the other parameters inconsistent.

Maximum spacing estimators are also at least as asymptotically efficient as maximum likelihood estimators, where the latter exist. However, MSEs may exist in cases where MLEs do not.[1]

Sensitivity

Maximum spacing estimators are sensitive to closely spaced observations, and especially ties.[6] Given

we get

When the ties are due to multiple observations, the repeated spacings (those that would otherwise be zero) should be replaced by the corresponding likelihood.[1] That is, one should substitute for , as

since .

When ties are due to rounding error, Template:Harvtxt suggest another method to remove the effects.[note 2] Given r tied observations from xi to xi+r−1, let δ represent the round-off error. All of the true values should then fall in the range . The corresponding points on the distribution should now fall between and . Cheng and Stephens suggest assuming that the rounded values are uniformly spaced in this interval, by defining

The MSE method is also sensitive to secondary clustering.[6] One example of this phenomenon is when a set of observations is thought to come from a single normal distribution, but in fact comes from a mixture normals with different means. A second example is when the data is thought to come from an exponential distribution, but actually comes from a gamma distribution. In the latter case, smaller spacings may occur in the lower tail. A high value of M(θ) would indicate this secondary clustering effect, and suggesting a closer look at the data is required.[6]

Goodness of fit

The statistic Sn(θ) is also a form of Moran or Moran-Darling statistic, M(θ), which can be used to test goodness of fit.[note 3] It has been shown that the statistic, when defined as

is asymptotically normal, and that a chi-squared approximation exists for small samples.[6] In the case where we know the true parameter , Template:Harvtxt show that the statistic has a normal distribution with

where γ is the Euler–Mascheroni constant which is approximately 0.57722.[note 4]

The distribution can also be approximated by that of , where

,

in which

and where follows a chi-squared distribution with degrees of freedom. Therefore, to test the hypothesis that a random sample of values comes from the distribution , the statistic can be calculated. Then should be rejected with significance if the value is greater than the critical value of the appropriate chi-squared distribution.[6]

Where θ0 is being estimated by , Template:Harvtxt showed that has the same asymptotic mean and variance as in the known case. However, the test statistic to be used requires the addition of a bias correction term and is:

where is the number of parameters in the estimate.

Generalized maximum spacing

Alternate measures and spacings

Template:Harvtxt generalized the MSE method to approximate other measures besides the Kullback–Leibler measure. Template:Harvtxt further expanded the method to investigate properties of estimators using higher order spacings, where an m-order spacing would be defined as .

Multivariate distributions

Template:Harvtxt discuss extended maximum spacing methods to the multivariate case. As there is no natural order for , they discuss two alternative approaches: a geometric approach based on Dirichlet cells and a probabilistic approach based on a “nearest neighbor ball” metric.

See also

Notes

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References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

Works Cited

Template:Refbegin

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    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

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    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang Note: linked paper is an updated 2001 version.
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    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

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