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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 Vuong's closeness test ： ウィキペディア英語版 Vuong's closeness test In statistics, the Vuong closeness test is likelihood-ratio-based test for model selection using the Kullback-Leibler information criterion. This statistic makes probabilistic statements about two models. They can be nested, non-nested or overlapping. The statistic tests the null hypothesis that the two models are equally close to the true data generating process, against the alternative that one model is closer. It cannot make any decision whether the "closer" model is the true model. With non-nested models and iid exogenous variables, model 1 (2) is preferred with significance level α, if the z statistic :$Z=\backslash frac)\}$ with : $)\}\; =\; L^1\_N-L^2\_N-\backslash frac\; \backslash log\; N$ exceeds the positive (falls below the negative) (1 − α)-quantile of the standard normal distribution. Here ''K''1 and ''K''2 are the numbers of parameters in models 1 and 2 respectively. The numerator is the difference between the maximum likelihoods of the two models, corrected for the number of coefficients analogous to the BIC, the term in the denominator of the expression for ''Z'', $\backslash omega\_N\; \backslash ,$, is defined by setting $\backslash omega\_N^2$ equal to either the mean of the squares of the pointwise log-likelihood ratios $\backslash ell\_i\backslash ,$, or to the sample variance of these values, where :$\backslash ell\_i\; =\; \backslash log\backslash frac.$ For nested or overlapping models the statistic : $2LR\_N(\backslash beta\_,\backslash beta\_)\backslash ,$ has to be compared to critical values from a weighted sum of chi squared distributions. This can be approximated by a gamma distribution: :$M\_m(.,\backslash bold\backslash lambda)\backslash sim\; \backslash Gamma(b,p)\backslash ,$ with : $\backslash bold\backslash lambda=(\backslash lambda\_1,\; \backslash lambda\_2,\; \backslash dots,\; \backslash lambda\_m),\backslash ,$ : $m=K\_1+K\_2,\backslash \; b=\backslash frac\; 1\; 2\; \backslash frac$ and : $p=\backslash frac\; 1\; 2\; \backslash frac\; ^2\}\; .$ $\backslash bold\backslash lambda$ is a vector of eigenvalues of a matrix of conditional expectations. The computation is quite difficult, so that in the overlapping and nested case many authors} only derive statements from a subjective evaluation of the Z statistic (is it subjectively "big enough" to accept my hypothesis?). Vuong's test for non-nested models has sometimes been used to determine whether zero-inflation is present in data. As a given model and its zero-inflated counterpart are not non-nested, this is an erroneous use of the test ==References== * * * 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「Vuong's closeness test」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.