翻訳と辞書 Words near each other ・ Scordia ・ Scordia Airfield ・ Scordisci ・ Scordyliodes ・ SCORE ・ Score ・ Score (Dream Theater album) ・ Score (film) ・ Score (game) ・ SCORE (Geo TV) ・ Score (music) ・ Score (Paul Haslinger album) ・ SCORE (satellite) ・ SCORE (software) ・ Score (sport) ・ Score (statistics) ・ SCORE (television) ・ SCORE Association ・ Score bug ・ SCORE Class 1 ・ SCORE Class 1/2-1600 ・ SCORE Class 10 ・ SCORE Class 11 ・ SCORE Class 2 ・ SCORE Class 3 ・ SCORE Class 4 ・ SCORE Class 5 ・ SCORE Class 5-1600 ・ SCORE Class 6 ・ SCORE Class 7SX Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Score (statistics) ： ウィキペディア英語版 Score (statistics) In statistics, the score, score function, efficient score〔Cox & Hinkley (1974), p 107〕 or informant indicates how sensitively a likelihood function $L(\backslash theta;\; X)$ depends on its parameter $\backslash theta$. Explicitly, the score for $\backslash theta$ is the gradient of the log-likelihood with respect to $\backslash theta$. The score plays an important role in several aspects of inference. For example: : *in formulating a test statistic for a locally most powerful test;〔Cox & Hinkley (1974), p 113〕 : *in approximating the error in a maximum likelihood estimate;〔Cox & Hinkley (1974), p 295〕 : *in demonstrating the asymptotic sufficiency of a maximum likelihood estimate;〔 : *in the formulation of confidence intervals;〔Cox & Hinkley (1974), p 222–3〕 : *in demonstrations of the Cramér–Rao inequality.〔Cox & Hinkley (1974), p 254〕 The score function also plays an important role in computational statistics, as it can play a part in the computation of maximum likelihood estimates. ==Definition== The score or efficient score 〔 is the gradient (the vector of partial derivatives), with respect to some parameter $\backslash theta$, of the logarithm (commonly the natural logarithm) of the likelihood function (the log-likelihood). If the observation is $X$ and its likelihood is $L(\backslash theta;X)$, then the score $V$ can be found through the chain rule: :$$ V \equiv V(\theta, X) = \frac \log L(\theta;X) = \frac \frac. Thus the score $V$ indicates the sensitivity of $L(\backslash theta;X)$ (its derivative normalized by its value). Note that $V$ is a function of $\backslash theta$ and the observation $X$, so that, in general, it is not a statistic. However in certain applications, such as the score test, the score is evaluated at a specific value of $\backslash theta$ (such as a null-hypothesis value, or at the maximum likelihood estimate of $\backslash theta$), in which case the result is a statistic. In older literature, the term "linear score" may be used to refer to the score with respect to infinitesimal translation of a given density. This convention arises from a time when the primary parameter of interest was the mean or median of a distribution. In this case, the likelihood of an observation is given by a density of the form $L(\backslash theta;X)=f(X+\backslash theta)$. The "linear score" is then defined as :$$ V_ = \frac \log f(X) 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「Score (statistics)」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.