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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 lemma ： ウィキペディア英語版 Stein's lemma Stein's lemma,〔Ingersoll, J., ''Theory of Financial Decision Making'', Rowman and Littlefield, 1987: 13-14.〕 named in honor of Charles Stein, is a theorem of probability theory that is of interest primarily because of its applications to statistical inference — in particular, to James–Stein estimation and empirical Bayes methods — and its applications to portfolio choice theory. The theorem gives a formula for the covariance of one random variable with the value of a function of another, when the two random variables are jointly normally distributed. ==Statement of the lemma== Suppose ''X'' is a normally distributed random variable with expectation μ and variance σ2. Further suppose ''g'' is a function for which the two expectations E(''g''(''X'') (''X'' − μ) ) and E( ''g'' ′(''X'') ) both exist (the existence of the expectation of any random variable is equivalent to the finiteness of the expectation of its absolute value). Then :$E\backslash bigl(g(X)(X-\backslash mu)\backslash bigr)=\backslash sigma^2\; E\backslash bigl(g\text{'}(X)\backslash bigr).$ In general, suppose ''X'' and ''Y'' are jointly normally distributed. Then :$\backslash operatorname(g(X),Y)=E(g\text{'}(X))\; \backslash operatorname(X,Y).$ 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 lemma」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.