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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 Chapman–Robbins bound ： ウィキペディア英語版 Chapman–Robbins bound In statistics, the Chapman–Robbins bound or Hammersley–Chapman–Robbins bound is a lower bound on the variance of estimators of a deterministic parameter. It is a generalization of the Cramér–Rao bound; compared to the Cramér–Rao bound, it is both tighter and applicable to a wider range of problems. However, it is usually more difficult to compute. The bound was independently discovered by John Hammersley in 1950, and by Douglas Chapman and Herbert Robbins in 1951. == Statement == Let be an unknown, deterministic parameter, and let be a random variable, interpreted as a measurement of ''θ''. Suppose the probability density function of ''X'' is given by ''p''(''x''; ''θ''). It is assumed that ''p''(''x''; ''θ'') is well-defined and that for all values of ''x'' and ''θ''. Suppose ''δ''(''X'') is an unbiased estimate of an arbitrary scalar function of ''θ'', i.e., :$E\_\backslash \; =\; g(\backslash theta)\backslash text\backslash theta.\backslash ,$ The Chapman–Robbins bound then states that :$\backslash mathrm\_(\backslash delta(X))\; \backslash ge\; \backslash sup\_\backslash Delta\; \backslash frac\; -\; 1\; \backslash right\; )^2\}.$ Note that the denominator in the lower bound above is exactly the $\backslash chi^2$-divergence of $p(\backslash cdot;\; \backslash theta+\backslash Delta)$ with respect to $p(\backslash cdot;\; \backslash theta)$. 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「Chapman–Robbins bound」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.