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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 Lehmann–Scheffé theorem ： ウィキペディア英語版 Lehmann–Scheffé theorem In statistics, the Lehmann–Scheffé theorem is prominent statement, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation.〔 The theorem states that any estimator which is unbiased for a given unknown quantity and that depends on the data only through a complete, sufficient statistic is the unique best unbiased estimator of that quantity. The Lehmann–Scheffé theorem is named after Erich Leo Lehmann and Henry Scheffé, given their two early papers.〔〔 If ''T'' is a complete sufficient statistic for ''θ'' and E(''g''(''T'')) = ''τ''(''θ'') then ''g''(''T'') is the uniformly minimum-variance unbiased estimator (UMVUE) of ''τ''(''θ''). ==Statement== Let $\backslash vec=\; X\_1,\; X\_2,\; \backslash dots,\; X\_n$ be a random sample from a distribution that has p.d.f (or p.m.f in the discrete case) $f(x:\backslash theta)$ where $\backslash theta\; \backslash in\; \backslash Omega$ is a parameter in the parameter space. Suppose $Y\; =\; u(\backslash vec)$ is a sufficient statistic for ''θ'', and let $\backslash$ be a complete family. If $\backslash phi:\backslash mathbb()\; =\; \backslash theta$ then $\backslash phi(Y)$ is the unique MVUE of ''θ''. 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「Lehmann–Scheffé theorem」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.