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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 Stein's unbiased risk estimate ： ウィキペディア英語版 Stein's unbiased risk estimate In statistics, Stein's unbiased risk estimate (SURE) is an unbiased estimator of the mean-squared error of "a nearly arbitrary, nonlinear biased estimator."〔 In other words, it provides an indication of the accuracy of a given estimator. This is important since the true mean-squared error of an estimator is a function of the unknown parameter to be estimated, and thus cannot be determined exactly. The technique is named after its discoverer, Charles Stein.〔 〕 == Formal statement == Let $\backslash mu\; \backslash in\; ^d$ be an unknown parameter and let $x\; \backslash in\; ^d$ be a measurement vector whose components are independent and distributed normally with mean $\backslash mu$ and variance $\backslash sigma^2$. Suppose $h(x)$ is an estimator of $\backslash mu$ from $x$, and can be written $h(x)\; =\; x\; +\; g(x)$, where $g$ is weakly differentiable. Then, Stein's unbiased risk estimate is given by :$\backslash mathrm(h)\; =\; d\backslash sigma^2\; +\; \backslash |g(x)\backslash |^2\; +\; 2\; \backslash sigma^2\; \backslash sum\_^d\; \backslash frac\; g\_i(x),$ where $g\_i(x)$ is the $i$th component of the function $g(x)$, and $\backslash |\backslash cdot\backslash |$ is the Euclidean norm. The importance of SURE is that it is an unbiased estimate of the mean-squared error (or squared error risk) of $h(x)$, i.e. :$E\_\backslash mu\; \backslash \; =\; \backslash mathrm(h),\backslash ,\backslash !$ with :$\backslash mathrm(h)\; =\; E\_\backslash mu\; \backslash |h(x)-\backslash mu\backslash |^2.$ Thus, minimizing SURE can act as a surrogate for minimizing the MSE. Note that there is no dependence on the unknown parameter $\backslash mu$ in the expression for SURE above. Thus, it can be manipulated (e.g., to determine optimal estimation settings) without knowledge of $\backslash mu$. 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「Stein's unbiased risk estimate」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.