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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 Basu's theorem ： ウィキペディア英語版 Basu's theorem In statistics, Basu's theorem states that any boundedly complete sufficient statistic is independent of any ancillary statistic. This is a 1955 result of Debabrata Basu.〔Basu (1955)〕 It is often used in statistics as a tool to prove independence of two statistics, by first demonstrating one is complete sufficient and the other is ancillary, then appealing to the theorem. An example of this is to show that the sample mean and sample variance of a normal distribution are independent statistics, which is done in the Examples section below. This property (independence of sample mean and sample variance) characterizes normal distributions. == Statement == Let ''Pθ'' be a family of distributions on a measurable space (''X, Σ''). Then if ''T'' is a boundedly complete sufficient statistic for ''θ'', and ''A'' is ancillary to ''θ'', then ''T'' is independent of ''A''. 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「Basu's 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.