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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 Mallows's Cp ： ウィキペディア英語版 Mallows's Cp In statistics, Mallows's ''Cp'', named for Colin Lingwood Mallows, is used to assess the fit of a regression model that has been estimated using ordinary least squares. It is applied in the context of model selection, where a number of predictor variables are available for predicting some outcome, and the goal is to find the best model involving a subset of these predictors. A small value of Cp means that the model is relatively precise. Mallows's ''Cp'' has been shown to be equivalent to Akaike information criterion in the special case of Gaussian linear regression. ==Definition and properties== Mallows's ''Cp'' addresses the issue of overfitting, in which model selection statistics such as the residual sum of squares always get smaller as more variables are added to a model. Thus, if we aim to select the model giving the smallest residual sum of squares, the model including all variables would always be selected. The ''Cp'' statistic calculated on a sample of data estimates the mean squared prediction error (MSPE) as its population target :$$ E\sum_j (\hat_j - E(Y_j\mid X_j))^2/\sigma^2, where $\backslash hat\_j$ is the fitted value from the regression model for the ''j''th case, ''E''(''Y''''j'' | ''X''''j'') is the expected value for the ''j''th case, and σ2 is the error variance (assumed constant across the cases). The MSPE will not automatically get smaller as more variables are added. The optimum model under this criterion is a compromise influenced by the sample size, the effect sizes of the different predictors, and the degree of collinearity between them. If ''P'' regressors are selected from a set of ''K'' > ''P'', the ''Cp'' statistic for that particular set of regressors is defined as: :$C\_p=\; -\; N\; +\; 2P,$ where *$SSE\_p\; =\; \backslash sum\_^N(Y\_i-Y\_)^2$ is the error sum of squares for the model with ''P'' regressors, *''Y''pi is the predicted value of the ''i''th observation of ''Y'' from the ''P'' regressors, *''S''2 is the residual mean square after regression on the complete set of ''K'' regressors and can be estimated by mean square error ''MSE'', * and ''N'' is the sample size. 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「Mallows's Cp」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.