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In [[statistics]], '''efficiency''' is a term used in the comparison of various statistical procedures and, in particular, it refers to a measure of the optimality of an [[estimator]], of an [[experimental design]]{{sfn|Everitt|2002|loc=p. 128}} or of a hypothesis testing procedure.<ref>{{SpringerEOM  | title= Efficiency of a statistical procedure| id=E/e035080 | last=Nikulin | first=M.S.}}</ref> Essentially, a more efficient estimator, experiment or test needs fewer samples than a less efficient one to achieve a given performance. This article primarily deals with efficiency of estimators.
<br><br>Pocket knives or folding knives make some of the most collectible knives, in component simply because their little nevertheless standard dimension makes it possible for for practical displays. If you choose to gather pocket knives, seem into particular display instances built exclusively to maintain them. Several collectible knives characteristic a themed take care of, this kind of as a movie character, cartoon, animal, or organization emblem. read a lot more Pocket knives as the title suggests is a knife that suits in your pocket, and it also folds in to its take care of. Generally these knives are no lager that five inches. But on situation they can be larger. These little knives have been utilised for several factors. read through far more<br>Swiss Military Knives are amount three. One of the finest things about Swiss Military is their reputation among nearly every person, youngsters, teenagers and grown ups. They are quite practical because of the many attachments and features they have. Some of the newer designs even have flash drives! Most are reasonably affordable so anybody [http://www.thebestpocketknifereviews.com/the-best-survival-knife-top-rated-wild-knives-in-the-world/ best survival knife in the world] can pay for them. Swiss Army knives are extremely durable and if taken care of, can very last a lifestyle time. Hopefully this list has been valuable and can aid you make a educated choice. Some of the identify brands that created the honorable mention, but not the best three are Cold Metal, Maxam, Spyderco, Remington, Fury and Buck knives<br>Scenario Cutlery employs a unique sample amount to recognize their knives. This pattern number is stamped into the tang of the knife blade. With this pattern quantity you can discover out precisely which design your knife is. Whether or not it really is a trapper, stockman, peanut, or folding hunter. Every design has a exclusive number to determine it. Discover the sample amount on your knife, locate it on the chart, and know specifically which type you have. This knife characteristics a G10 textured manage for secure grip and is outfitted with speed-risk-free for one handed assisted opening. It also will come with a S30V stainless metal blade provides toughness with a great top quality complete.<br>In our everyday life we cannot deny the significance of knives These are possibly one of the wonderful inventions in instruments and hardware category. Regardless of whether it's a kitchen requirement or it's essential in gardening we have to use them often. By employing this tool or equipment we get a whole lot advantages. It's always greater to have a expert set of these chopping tools. But at the very same time we ought to be careful whilst making use of these so that we can avert significant accidents. In my view, the answer would be a resounding Indeed, I can't imagine why somebody would not want the ease of possessing a pocket knife on their man or woman.<br>Folding knives regularly come offered with a a single handed opening attribute by employing a little thumb lever, or a hole in the blade to place the thumb into. This can make the knife usable with possibly hand, and will increase the [http://wachstumswende.sinnwerkstatt.com/index.php?title=Wilderness_Survival_Knife mobility] of the hunter. Folding knives also have a lock feature that boosts protection throughout use. These knives are typically smaller in dimensions and suit neatly into a pocket or little belt sheath. Several folders also come equipped with a pocket or belt clip so they can be worn on the outside the house of clothing for quicker entry. <br>The drop stage knife is an superb layout for the huge game hunter. This style normally functions a strong, curved blade of reasonably thick steel. These characteristics enable the consumer to lower the skin off the animal utilizing the total edge of the knife, rather than just the level. This permits for rapid skinning and extremely small injury to the meat. The design of the fall point also allows for other discipline cleaning jobs this kind of as gutting and the splitting of the rib cage or pelvis, although a observed or hatchet is the desired technique for the latter two duties.<br>A “Liner Lock” is a folding “lockback” knife you can open and near with one hand. A thumb-gap or thumb-stud opens the blade. It locks open making use of a tensioned metallic liner inside the handle. To release the blade, area your thumb on the front part of the liner and drive to the remaining. Body Lock – A single [http://www.thebestpocketknifereviews.com/the-best-survival-knife-top-rated-wild-knives-in-the-world/ Best survival knife]-Hander A “Frame Lock” is a one-hand opening knife. Only the lock is a tensioned element of the deal with body with an open up channel. When the blade opens, the body lock moved into the manage opening, locking in opposition to the blade. To release, thrust the liner to the still left. The Buck Assisted Opening Knife<br>Spyderco is one more attempted and dependable knife company which is well-known with fans. Their knives are instantaneously recognizable and ergonomically sound. The Spyderco Tenacious has been around for a number of several years now and represents incredible value for income. It’s a tactical knife which can be used as an EDC and features a leaf-formed 8CR13MOV steel blade that’s relatively broad but plenty sharp. The Tenacious performs effectively in most programs like some large obligation duties and with extremely small blade play in possibly path. The G-10 take care of is skeletonized stainless metal which minimizes weight without expensing also much toughness and matches cosy in your hand. SOG Flash II.<br>Properly, I guess I am somewhat outdated trend when it comes to knives To me, carrying a pocket knife is correct up there with shaking a mans hand. It is also like a appropriate of passage from boyhood to manhood. Being permitted to have your knife is a signal of a boy becoming some thing far more than just a boy. The only time I do not have a knife with me is when I know I am going someplace they may possibly want to confiscate it like at a concert for occasion. When this transpires, it goes in the glove box of my truck right next to my Leatherman multi-instrument.
 
The '''relative efficiency''' of two procedures is the ratio of their efficiencies, although often this term is used where the comparison is made between a given procedure and a notional "best possible" procedure. The efficiencies and the relative efficiency of two procedures theoretically depend on the sample size available for the given procedure, but it is often possible to use the '''asymptotic relative efficiency''' (defined as the limit of the relative efficiencies as the sample size grows) as the principal comparison measure.
 
Efficiencies are often defined using the [[variance]] or [[mean square error]] as the measure of desirability.{{sfn|Everitt|2002|loc=p. 128}}
 
==Estimators==
 
The efficiency of an [[bias of an estimator|unbiased]] [[estimator]], ''T'', of a [[statistical parameter|parameter]] ''&theta;'' is defined as{{cn|date=April 2013}}
 
:<math>
e(T)
=
\frac{1/\mathcal{I}(\theta)}{\mathrm{var}(T)}
</math>
 
where <math>\mathcal{I}(\theta)</math> is the [[Fisher information]] of the sample.
Thus ''e''(''T'') is the minimum possible variance for an unbiased estimator divided by its actual variance. The [[Cramér–Rao bound]] can be used to prove that  ''e''(''T'')&nbsp;≤&nbsp;1.
 
===Efficient estimators===
{{Main|efficient estimator}}
If an [[estimator bias|unbiased]] [[estimator]] of a parameter ''&theta;'' attains <math>e(T) = 1</math> for all values of the parameter, then the estimator is called efficient.{{Citation needed|date=January 2012}}
 
Equivalently, the estimator achieves equality in the [[Cramér–Rao inequality]] for all ''&theta;''.
 
An efficient estimator is also the [[minimum variance unbiased estimator]] (MVUE).
This is because an efficient estimator maintains equality on the Cramér–Rao inequality for all parameter values, which means it attains the minimum variance for all parameters (the definition of the MVUE). The MVUE estimator, even if it exists, is not necessarily efficient, because "minimum" does not mean equality holds on the Cramér–Rao inequality.
 
Thus an efficient estimator need not exist, but if it does, it is the MVUE.
 
===Asymptotic efficiency===
For some [[estimator]]s, they can attain efficiency [[asymptotically]] and are thus called asymptotically efficient estimators.
This can be the case for some [[maximum likelihood]] estimators or for any estimators that attain equality of the Cramér–Rao bound asymptotically.
 
====Example====
Consider a sample of size <math>N</math> drawn from a [[normal distribution]] of mean <math>\mu</math> and unit [[variance]], i.e., <math>X_n \sim \mathcal{N}(\mu, 1).</math>
 
The [[sample mean]], <math>\overline{X}</math>, of the sample <math>X_1, X_2, \ldots, X_N</math>, defined as
 
:<math>
\overline{X} = \frac{1}{N} \sum_{n=1}^{N} X_n \sim \mathcal{N}\left(\mu, \frac{1}{N}\right).
</math>
 
The variance of the mean, 1/''N'' (the square of the [[standard error]]) is equal to the reciprocal of the [[Fisher information]] from the sample and thus, by the [[Cramér–Rao inequality]], the sample mean is efficient in the sense that its efficiency is unity (100%).
 
Now consider the [[sample median]], <math>\widetilde{X}</math>.
This is an [[estimator bias|unbiased]] and [[Consistent estimator|consistent]] estimator for <math>\mu</math>.
For large <math>N</math> the sample median is approximately [[normal distribution|normally distributed]] with mean <math>\mu</math> and variance <math>{\pi}/{2N},</math> i.e.,<ref>Williams, D. (2001) ''Weighing the Odds'', CUP. ISBN 052100618X (p.165) </ref>
:<math>\widetilde{X} \sim \mathcal{N}\left(\mu, \frac{\pi}{2N}\right).</math>
The efficiency for large <math>N</math> is thus
:<math>
e\left(\widetilde{X}\right) = \left(\frac{1}{N}\right) \left(\frac{\pi}{2N}\right)^{-1} = 2/\pi \approx 64%.
</math>
Note that this is the [[asymptote|asymptotic]] efficiency &mdash; that is, the efficiency in the limit as sample size <math>N</math> tends to infinity. For finite values of <math>N,</math> the efficiency is higher than this (for example, a sample size of 3 gives an efficiency of about 74%).{{cn|date=April 2013}}
 
The sample mean is thus more efficient than the sample median in this example. However, there may be measures by which the median performs better. For example, the median is far more robust to [[outlier]]s, so that if the Gaussian model is questionable or approximate, there may advantages to using the median (see [[Robust statistics]]).
 
===Dominant estimators===
If <math>T_1</math> and <math>T_2</math> are estimators for the parameter <math>\theta</math>, then <math>T_1</math> is said to '''[[dominating decision rule|dominate]]''' <math>T_2</math> if:
# its [[mean squared error]] (MSE) is smaller for at least some value of <math>\theta</math>
# the MSE does not exceed that of <math>T_2</math> for any value of θ.
 
Formally, <math>T_1</math> dominates <math>T_2</math> if
:<math>
\mathrm{E}
\left[
(T_1 - \theta)^2
\right]
\leq
\mathrm{E}
\left[
(T_2-\theta)^2
\right]
</math>
 
holds for all <math>\theta</math>, with strict inequality holding somewhere.
 
===Relative efficiency===
The relative efficiency of two estimators is defined as
 
:<math>
e(T_1,T_2)
=
\frac
{\mathrm{E} \left[ (T_2-\theta)^2 \right]}
{\mathrm{E} \left[ (T_1-\theta)^2 \right]}
</math>
 
Although <math>e</math> is in general a function of <math>\theta</math>, in many cases the dependence drops out; if this is so, <math>e</math> being greater than one would indicate that <math>T_1</math> is preferable, whatever the true value of <math>\theta</math>.
 
An alternative to relative efficiency for comparing estimators, is the [[Pitman closeness criterion]]. This replaces the comparison of mean-squared-errors with comparing how often one estimator produces estimates closer to the true value than another estimator.
 
===Robustness===
Efficiency of an estimator may change significantly if the distribution changes, often dropping. This is one of the motivations of [[robust statistics]] – an estimator such as the sample mean is an efficient estimator of the population mean of a normal distribution, for example, but can be an inefficient estimator of a [[mixture distribution]] of two normal distributions with the same mean and different variances. For example, if a distribution is a combination of 98% ''N''(''μ,'' ''σ'') and 2% ''N''(''μ,'' 10''σ''), the presence of extreme values from the latter distribution (often "contaminating outliers") significantly reduces the efficiency of the sample mean as an estimator of ''μ.'' By contrast, the trimmed mean is less efficient for a normal distribution, but is more robust (less affected) by changes in distribution, and thus may be more efficient for a mixture distribution. Similarly, the shape of a distribution, such as [[skewness]] or heavy tails, can significantly reduce the efficiency of estimators that assume a symmetric distribution or thin tails.
 
===Uses of inefficient estimators===
{{see|L-estimator#Applications}}
 
While efficiency is a desirable quality of an estimator, it must be weighed against other desiderata, and an estimator that is efficient for certain distributions may well be inefficient for other distributions. Most significantly, estimators that are efficient for clean data from a simple distribution, such as the normal distribution (which is symmetric, unimodal, and has thin tails) may not be robust to contamination by outliers, and may be inefficient for more complicated distributions. In [[robust statistics]], more importance is placed on robustness and applicability to a wide variety of distributions, rather than efficiency on a single distribution. [[M-estimator]]s are a general class of solutions motivated by these concerns, yielding both robustness and high relative efficiency, though possibly lower efficiency than traditional estimators for some cases. These are potentially very computationally complicated, however.
 
A more traditional alternative are [[L-estimator]]s, which are very simple statistics that are easy to compute and interpret, in many cases robust, and often sufficiently efficient for initial estimates. See [[L-estimator#Applications|applications of L-estimators]] for further discussion.
 
==Hypothesis tests==
For comparing [[significance test]]s, a meaningful measure of efficiency can be defined based on the sample size required for the test to achieve a given [[statistical power|power]].{{sfn|Everitt|2002|loc=p. 321}}
 
[[Pitman efficiency]]<ref>{{SpringerEOM  | title=Efficiency, asymptotic | id=E/e035070  | last=Nikitin  | first=Ya.Yu.}}</ref> and  [http://www.encyclopediaofmath.org/index.php/Bahadur_efficiency Bahadur efficiency] (or [[Hodges–Lehmann efficiency]] )<ref>Arcones M.A. [http://www.math.binghamton.edu/arcones/prep/pv.pdf "Bahadur efficiency of the likelihood ratio test"] preprint</ref><ref>Canay I.A. & Otsu, T. [http://faculty.wcas.northwestern.edu/~iac879/wp/HL.pdf "Hodges-Lehmann Optimality for Testing Moment Condition Models"]</ref> relate to the comparison of the performance of [[Statistical hypothesis testing]] procedures. The Encyclopedia of Mathematics provides a [http://www.encyclopediaofmath.org/index.php/Efficiency,_asymptotic brief exposition] of these three criteria.
 
==Experimental design==
{{see|Optimal design}}
 
For experimental designs, efficiency relates to the ability of a design to achieve the objective of the study with minimal expenditure of resources such as time and money. In simple cases, the relative efficiency of designs can be expressed as the ratio of the sample sizes required to achieve a given objective.<ref>Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', OUP. ISBN 0-19-920613-9</ref>
 
See [[optimal design]] for further discussion.
 
==Notes==
{{reflist}}
 
==References==
*{{cite isbn|052181099X}}
*{{cite isbn|9780387985954}}
* {{SpringerEOM
| title=Efficiency, asymptotic
| id=E/e035070
| last=Nikitin
| first=Ya.Yu.
}}
{{refend}}
 
[[Category:Statistical theory]]
[[Category:Statistical terminology]]
 
[[de:Effizienz (Statistik)]]
[[es:Eficiencia (estadística)]]
[[it:Efficienza (statistica)]]
[[pt:Eficiência (estatística)]]

Latest revision as of 19:57, 23 November 2014



Pocket knives or folding knives make some of the most collectible knives, in component simply because their little nevertheless standard dimension makes it possible for for practical displays. If you choose to gather pocket knives, seem into particular display instances built exclusively to maintain them. Several collectible knives characteristic a themed take care of, this kind of as a movie character, cartoon, animal, or organization emblem. read a lot more Pocket knives as the title suggests is a knife that suits in your pocket, and it also folds in to its take care of. Generally these knives are no lager that five inches. But on situation they can be larger. These little knives have been utilised for several factors. read through far more
Swiss Military Knives are amount three. One of the finest things about Swiss Military is their reputation among nearly every person, youngsters, teenagers and grown ups. They are quite practical because of the many attachments and features they have. Some of the newer designs even have flash drives! Most are reasonably affordable so anybody best survival knife in the world can pay for them. Swiss Army knives are extremely durable and if taken care of, can very last a lifestyle time. Hopefully this list has been valuable and can aid you make a educated choice. Some of the identify brands that created the honorable mention, but not the best three are Cold Metal, Maxam, Spyderco, Remington, Fury and Buck knives
Scenario Cutlery employs a unique sample amount to recognize their knives. This pattern number is stamped into the tang of the knife blade. With this pattern quantity you can discover out precisely which design your knife is. Whether or not it really is a trapper, stockman, peanut, or folding hunter. Every design has a exclusive number to determine it. Discover the sample amount on your knife, locate it on the chart, and know specifically which type you have. This knife characteristics a G10 textured manage for secure grip and is outfitted with speed-risk-free for one handed assisted opening. It also will come with a S30V stainless metal blade provides toughness with a great top quality complete.
In our everyday life we cannot deny the significance of knives These are possibly one of the wonderful inventions in instruments and hardware category. Regardless of whether it's a kitchen requirement or it's essential in gardening we have to use them often. By employing this tool or equipment we get a whole lot advantages. It's always greater to have a expert set of these chopping tools. But at the very same time we ought to be careful whilst making use of these so that we can avert significant accidents. In my view, the answer would be a resounding Indeed, I can't imagine why somebody would not want the ease of possessing a pocket knife on their man or woman.
Folding knives regularly come offered with a a single handed opening attribute by employing a little thumb lever, or a hole in the blade to place the thumb into. This can make the knife usable with possibly hand, and will increase the mobility of the hunter. Folding knives also have a lock feature that boosts protection throughout use. These knives are typically smaller in dimensions and suit neatly into a pocket or little belt sheath. Several folders also come equipped with a pocket or belt clip so they can be worn on the outside the house of clothing for quicker entry.
The drop stage knife is an superb layout for the huge game hunter. This style normally functions a strong, curved blade of reasonably thick steel. These characteristics enable the consumer to lower the skin off the animal utilizing the total edge of the knife, rather than just the level. This permits for rapid skinning and extremely small injury to the meat. The design of the fall point also allows for other discipline cleaning jobs this kind of as gutting and the splitting of the rib cage or pelvis, although a observed or hatchet is the desired technique for the latter two duties.
A “Liner Lock” is a folding “lockback” knife you can open and near with one hand. A thumb-gap or thumb-stud opens the blade. It locks open making use of a tensioned metallic liner inside the handle. To release the blade, area your thumb on the front part of the liner and drive to the remaining. Body Lock – A single Best survival knife-Hander A “Frame Lock” is a one-hand opening knife. Only the lock is a tensioned element of the deal with body with an open up channel. When the blade opens, the body lock moved into the manage opening, locking in opposition to the blade. To release, thrust the liner to the still left. The Buck Assisted Opening Knife
Spyderco is one more attempted and dependable knife company which is well-known with fans. Their knives are instantaneously recognizable and ergonomically sound. The Spyderco Tenacious has been around for a number of several years now and represents incredible value for income. It’s a tactical knife which can be used as an EDC and features a leaf-formed 8CR13MOV steel blade that’s relatively broad but plenty sharp. The Tenacious performs effectively in most programs like some large obligation duties and with extremely small blade play in possibly path. The G-10 take care of is skeletonized stainless metal which minimizes weight without expensing also much toughness and matches cosy in your hand. SOG Flash II.
Properly, I guess I am somewhat outdated trend when it comes to knives To me, carrying a pocket knife is correct up there with shaking a mans hand. It is also like a appropriate of passage from boyhood to manhood. Being permitted to have your knife is a signal of a boy becoming some thing far more than just a boy. The only time I do not have a knife with me is when I know I am going someplace they may possibly want to confiscate it like at a concert for occasion. When this transpires, it goes in the glove box of my truck right next to my Leatherman multi-instrument.

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