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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 Mean dependence ： ウィキペディア英語版 Mean dependence In probability theory, a random variable ''Y'' is said to be mean independent of random variable ''X'' if and only if E(''Y''|''X'') = E(''Y'') for all ''x'' such that ''ƒ''1(''x'') is not equal to zero. ''Y'' is said to be mean dependent if ''E''(''Y''|''X'') ≠ ''μ''(''y'') for some ''x'' such that ''ƒ''1(''x'') is not equal to zero. According to and , Stochastic independence implies mean independence, but the converse is not necessarily true. Moreover, mean independence implies uncorrelation while the converse is not necessarily true. The concept of mean independence is often used in econometrics to have a middle ground between the strong assumption of independent variables $X\_1\; \backslash perp\{\}\; X\_2$ and the weak assumption of uncorrelated variables $\backslash text\{Cov\}(X\_1,X\_2)=0$ of a pair of random variables $X\_1$ and $X\_2$. If ''X'', ''Y'' are two different random variables such that ''X'' is mean independent of ''Y'' and ''Z=f(X)'', which means that ''Z'' is a function only of ''X'', then ''Y'' and ''Z'' are mean independent. ==References== * * Category:Statistical terminology 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「Mean dependence」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.