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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク James–Stein estimator ： ウィキペディア英語版 James–Stein estimator The James–Stein estimator is a biased estimator of the mean of Gaussian random vectors. It can be shown that the James–Stein estimator dominates the "ordinary" least squares approach, i.e., it has lower mean squared error on average. It is the best-known example of Stein's phenomenon. An earlier version of the estimator was developed by Charles Stein in 1956, and is sometimes referred to as Stein's estimator. The result was improved by Willard James and Charles Stein in 1961. == Setting == Suppose ''θ'' is an unknown parameter vector of length $m$, and let y be a vector of observations (also of length $m$), such that the observations are normally distributed: :$$ \sim N(, \sigma^2 I).\, We are interested in obtaining an estimate $\backslash widehat\; =\; \backslash widehat()$ of ''θ'', based on a single observation vector y. This is an everyday situation in which a set of parameters is measured, and the measurements are corrupted by independent Gaussian noise. Since the noise has zero mean, it is very reasonable to use the measurements themselves as an estimate of the parameters. This is the approach of the least squares estimator, which is $\backslash widehat\_\; =$. As a result, there was considerable shock and disbelief when Stein demonstrated that, in terms of mean squared error $E\; \backslash \; \backslash |^2\; \backslash \}$, this approach is suboptimal.〔 The result became known as Stein's phenomenon. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「James–Stein estimator」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.