en>Edokter: /* See also */

2013-03-09T08:58:14Z

See also

← Older revision		Revision as of 10:58, 9 March 2013
Line 1:		Line 1:
	I'~~m Elke~~ [~~http:~~//~~www~~.~~imyourbroker~~.~~com~~/~~%E4%B8%8A%E5%93%81-%E7%99%BB%E5%B1%B1%E3%83%BB%E3%83%88%E3%83%AC%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0-%E6%96%B0%E5%88%B0%E7%9D%80~~/~~%E8%B6%85%E3%83%81%E3%83%BC%E3%83%97-%E3%81%9D%E3%81%AE%E4%BB%96-%E6%96%B0%E7%9D%80 登山トレッキングその他]~~ and ~~was born on 20 August~~ [http://~~www~~.~~imyourbroker~~.~~com~~/~~%E8%B6%85%E7%BE%8E~~-~~%E3%83%95%E3%82%A3%E3%83%83%E3%82%B7%E3%83%B3%E3%82%B0~~-~~%E3%82%AA%E3%83%B3%E3%83%A9%E3%82%A4%E3%83%B3%E3%82%B7%E3%83%A7%E3%83%83%E3%83%97~~/~~%E7%89%B9%E3%81%AB%E5%A3%B2%E3%82%8C%E3%81%A6%E3%81%84%E3%82%8B~~-~~%E3%83%AB%E3%82%A2%E3%83%BC%E7%94%A8%E5%93%81-%E3%82%B9%E3%83%88%E3%82%A2~~/~~%E4%BD%8E%E4%BE%A1%E6%A0%BC-%E3%83%A9%E3%83%B3%E3%83%87%E3%82%A3%E3%83%B3%E3%82%B0%E3%83%84%E3%83%BC%E3%83%AB-%E6%96%B0%E5%93%81~~/%E4%BF%A1%E9%A0%BC-%E3%83%A9%E3%83%B3%E3%83%87%E3%82%A3%E3%83%B3%E3%82%B0%E3%82%B7%E3%83%A3%E3%83%95%E3%83%88%E3%83%BB%E3%83%8D%E3%83%83%E3%83%88%E3%83%BB%E3%82%AE%E3%83%A3%E3%83%95-%E6%96%B0%E5%93%81 フィッシングランディングシャフトネットギャフ] 1972. ~~My hobbies~~ are ~~Seaglass collecting~~ and ~~[http:~~/~~/www~~.~~imyourbroker~~.~~com/%E4%B8%8A%E5%93%81~~-~~%E7%99%BB%E5%B1%B1%E3%83%BB%E3%83%88%E3%83%AC%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0~~-~~%E6%96%B0%E5%88%B0%E7%9D%80/%E9%AB%98%E7%B4%9A~~-~~%E3%83%A1%E3%83%B3%E3%82%BA%E3%82%BB%E3%83%83%E3%83%88-%E5%93%81%E8%B3%AA%E6%BA%80%E7%82%B9~~/~~%E5%90%84%E5%BF%85%E8%A6%81%E3%82%92%E6%BA%80%E8%B6%B3%E3%81%99%E3%82%8B~~-%E8%A3%85%E5%82%99%E3%83%99%E3%82%B9%E3%83%88%EF%BC%92%E7%82%B9%E3%82%BB%E3%83%83%E3%83%88-%E5%93%81%E8%B3%AA%E6%BA%80%E7%82%B9/%E4%BD%8E%E4%BE%A1%E6%A0%BC-%E9%9B%A8%E5%85%B7%EF%BC%8B%E3%83%96%E3%83%BC%E3%83%84-%E5%8E%B3%E9%81%B8%E3%81%97%E5%88%B6%E4%BD%9C%E3%81%97%E3%81%9F 登山トレッキング雨具＋ブーツ] Australian Football League.<br><br>~~Also visit my web site~~ ... ~~[http://www~~.~~imyourbroker~~.~~com/%E8%B6%85%E7%BE%8E~~-~~%E3%83%95%E3%82%A3%E3%83%83%E3%82%B7%E3%83%B3%E3%82%B0-%E3%82%AA%E3%83%B3%E3%83%A9%E3%82%A4%E3%83%B3%E3%82%B7%E3%83%A7%E3%83%83%E3%83%97~~/~~%E8%B6%85%E3%83%81%E3%83%BC%E3%83%97~~-~~%E3%82%AA%E3%83%95%E3%82%B7%E3%83%A7%E3%82%A2%E3%83%AD%E3%83%83%E3%83%89-%E6%BA%80%E8%BC%89~~/~~%E9%AB%98%E7%B4%9A~~-~~%E3%82%A8%E3%82%A4%E3%83%86%E3%83%83%E3%82%AF~~-%E3%82%BB%E3%83%BC%E3%83%AB%E3%82%B9/%E5%8F%B2%E4%B8%8A%E6%9C%80%E3%82%82%E6%BF%80%E5%AE%89%E3%81%84-%E3%83%86%E3%82%A4%E3%83%AB%E3%82%A6%E3%82%A9%E3%83%BC%E3%82%AF%E3%83%BB%E3%82%B7%E3%83%BC%E3%83%AB%E3%82%BA%EF%BC%B8%EF%BC%94%EF%BC%98-%E4%B8%80%E7%95%AA%E5%93%81%E8%B3%AA フィッシング史上最も激テイルウォークシールズＸ４８]		In [[statistical theory]], the field of '''high-dimensional statistics''' studies data whose [[dimension]] is larger than dimensions considered in classical [[multivariate analysis]]. High-dimensional statistics relies on the [[probability theory\|theory]] of [[random element\|random vector]]s. In many applications, the dimension of the data vectors may be larger than the [[sample size]].

			==History==

			Traditionally, [[statistical inference]] considers a probability model for a population and considers data that arose as a sample from the population. For many problems, the estimates of the population characteristics ("parameters") can be substantially refined (in theory) as the sample size increases toward infinity. A traditional requirement of estimators is [[Consistency (statistics)\|consistency]], that is, the convergence to the unknown true value of the parameter.

			In 1968, A.N.[[Kolmogorov]] proposed another setting of statistical problems and another setting for the asymptotics, in which the dimension of variables ''p'' increases along with the sample size ''n'' so that the ratio ''p''/''n'' tends to a constant. It was called the “increasing dimension asymptotics” or “the Kolmogorov asymptotics”<ref>S. A. Aivasian, V. M. Buchstaber, I. S. Yenyukov, L. D. Meshalkin. Applied Statistics. Classification and Reduction of Dimensionality. Moscow, 1989 (in Russian).</ref> Kolmogorov's approach makes it possible to isolate many principal terms of error probabilities and of standard measures of the quality of estimators (quality functions) for large ''p'' and ''n''.

			Recently, researchers are more interested in even larger dimension cases, e.g. <math>p = O(\exp(n^a))</math>, where <math>0<a<1</math>. This field emerges from the need of extracting meaningful information from many different areas.

			==Mathematical theory==

			Extensive mathematical investigations were carried out that resulted in the creation of systematic theory for improved and asymptotically unimprovable versions of multivariate statistical procedures (see
			references at <ref>[http://hd-stat.narod.ru http://hd-stat.narod.ru 'HIGH-DIMENSIONAL (HD-) STATISTICS'].</ref>). A special parameter ''G'' that is a function of the fourth moments of variables
			was found having the property that a small value of ''G'' produces a number of specifically many-parametric phenomena. For increasing ''p'' and ''n'' so that ''p''/''n'' tends to a constant and ''G'' → 0, the principal terms of rotation invariant functionals occurring in statistics prove to be dependent on only the first two moments of variables. Under ''n'' and ''p'' tending to infinity, ''p''/''n'' → ''y'' > 0, and ''G'' → 0, these functionals have vanishing variance and converge to constants that represent the limit value of empirical means and
			variances. As a consequence, some stable integral relations are produced between functions of parameters and functions of observable variables. They were called “stochastic canonical equations” or “dispersion equations”.<ref>V.L.Girko. Canonical Stochastic Equations, vol. 1,2, Kluwer Academic Publishers, Dordrecht, 2000.</ref> Using them one can express the principle parts of standard quality functions of regularized multivariate statistical procedures as functions of only observed variables. This provides
			the possibility of choosing better procedures and finding asymptotically unimprovable solutions.

			==Current developments==
			High-dimensional statistics has been the focus of many seminars and workshops.<ref>Program on High-Dimensional Inference for 2006-2007. SAMSI, USA.</ref><ref>Workshop in High-Dimensional Data Analysis, National University of Singapore. February, 2008.</ref><ref>Workshops HD-statistics in biology, Isaac Newton Inst. for Math. Sci., Cambridge. 31.03-27.06 2008.</ref><ref>Young European Statistics Workshop (YES-2), Eindhoven, Netherland. June, 2008.</ref>

			==Notes==
			{{Reflist}}

			== References ==

			* {{cite book\|title= High-dimensional data analysis\|year=2011 \|editor= T. Tony Cai, Xiaotong Shen \|publisher = World Scientific\|location = Singapore\|series= Frontiers of Statistics\|ref=harv}}

			* {{cite book\|author= Peter Bühlmann and Sara van de Geer\|title=Statistics for high-dimensional data: methods, theory and applications\|publisher=Springer\|location=Heidelberg; New York\|year=2011\|ref=harv}}

			{{statistics\|state=collapsed}}

			[[Category:Multivariate statistics]]
			[[Category:Decision theory]]
			[[Category:Probability theory]]
			[[Category:Functional analysis]]

en>Kri: /* See also */ bigmath -> mvar

2012-06-07T22:20:43Z

See also: bigmath -> mvar

New page

I'm Elke [http://www.imyourbroker.com/%E4%B8%8A%E5%93%81-%E7%99%BB%E5%B1%B1%E3%83%BB%E3%83%88%E3%83%AC%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0-%E6%96%B0%E5%88%B0%E7%9D%80/%E8%B6%85%E3%83%81%E3%83%BC%E3%83%97-%E3%81%9D%E3%81%AE%E4%BB%96-%E6%96%B0%E7%9D%80 登山トレッキングその他] and was born on 20 August [http://www.imyourbroker.com/%E8%B6%85%E7%BE%8E-%E3%83%95%E3%82%A3%E3%83%83%E3%82%B7%E3%83%B3%E3%82%B0-%E3%82%AA%E3%83%B3%E3%83%A9%E3%82%A4%E3%83%B3%E3%82%B7%E3%83%A7%E3%83%83%E3%83%97/%E7%89%B9%E3%81%AB%E5%A3%B2%E3%82%8C%E3%81%A6%E3%81%84%E3%82%8B-%E3%83%AB%E3%82%A2%E3%83%BC%E7%94%A8%E5%93%81-%E3%82%B9%E3%83%88%E3%82%A2/%E4%BD%8E%E4%BE%A1%E6%A0%BC-%E3%83%A9%E3%83%B3%E3%83%87%E3%82%A3%E3%83%B3%E3%82%B0%E3%83%84%E3%83%BC%E3%83%AB-%E6%96%B0%E5%93%81/%E4%BF%A1%E9%A0%BC-%E3%83%A9%E3%83%B3%E3%83%87%E3%82%A3%E3%83%B3%E3%82%B0%E3%82%B7%E3%83%A3%E3%83%95%E3%83%88%E3%83%BB%E3%83%8D%E3%83%83%E3%83%88%E3%83%BB%E3%82%AE%E3%83%A3%E3%83%95-%E6%96%B0%E5%93%81 フィッシングランディングシャフトネットギャフ] 1972. My hobbies are Seaglass collecting and [http://www.imyourbroker.com/%E4%B8%8A%E5%93%81-%E7%99%BB%E5%B1%B1%E3%83%BB%E3%83%88%E3%83%AC%E3%83%83%E3%82%AD%E3%83%B3%E3%82%B0-%E6%96%B0%E5%88%B0%E7%9D%80/%E9%AB%98%E7%B4%9A-%E3%83%A1%E3%83%B3%E3%82%BA%E3%82%BB%E3%83%83%E3%83%88-%E5%93%81%E8%B3%AA%E6%BA%80%E7%82%B9/%E5%90%84%E5%BF%85%E8%A6%81%E3%82%92%E6%BA%80%E8%B6%B3%E3%81%99%E3%82%8B-%E8%A3%85%E5%82%99%E3%83%99%E3%82%B9%E3%83%88%EF%BC%92%E7%82%B9%E3%82%BB%E3%83%83%E3%83%88-%E5%93%81%E8%B3%AA%E6%BA%80%E7%82%B9/%E4%BD%8E%E4%BE%A1%E6%A0%BC-%E9%9B%A8%E5%85%B7%EF%BC%8B%E3%83%96%E3%83%BC%E3%83%84-%E5%8E%B3%E9%81%B8%E3%81%97%E5%88%B6%E4%BD%9C%E3%81%97%E3%81%9F 登山トレッキング雨具＋ブーツ] Australian Football League.<br><br>Also visit my web site ... [http://www.imyourbroker.com/%E8%B6%85%E7%BE%8E-%E3%83%95%E3%82%A3%E3%83%83%E3%82%B7%E3%83%B3%E3%82%B0-%E3%82%AA%E3%83%B3%E3%83%A9%E3%82%A4%E3%83%B3%E3%82%B7%E3%83%A7%E3%83%83%E3%83%97/%E8%B6%85%E3%83%81%E3%83%BC%E3%83%97-%E3%82%AA%E3%83%95%E3%82%B7%E3%83%A7%E3%82%A2%E3%83%AD%E3%83%83%E3%83%89-%E6%BA%80%E8%BC%89/%E9%AB%98%E7%B4%9A-%E3%82%A8%E3%82%A4%E3%83%86%E3%83%83%E3%82%AF-%E3%82%BB%E3%83%BC%E3%83%AB%E3%82%B9/%E5%8F%B2%E4%B8%8A%E6%9C%80%E3%82%82%E6%BF%80%E5%AE%89%E3%81%84-%E3%83%86%E3%82%A4%E3%83%AB%E3%82%A6%E3%82%A9%E3%83%BC%E3%82%AF%E3%83%BB%E3%82%B7%E3%83%BC%E3%83%AB%E3%82%BA%EF%BC%B8%EF%BC%94%EF%BC%98-%E4%B8%80%E7%95%AA%E5%93%81%E8%B3%AA フィッシング史上最も激テイルウォークシールズＸ４８]

Template:Bigmath/doc - Revision history

en>Edokter: /* See also */

en>Kri: /* See also */ bigmath -> mvar