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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 Chow test ： ウィキペディア英語版 Chow test The Chow test is a statistical and econometric test of whether the coefficients in two linear regressions on different data sets are equal. The Chow test was invented by economist Gregory Chow in 1960. In econometrics, the Chow test is most commonly used in time series analysis to test for the presence of a structural break. In program evaluation, the Chow test is often used to determine whether the independent variables have different impacts on different subgroups of the population. Suppose that we model our data as :$$ y_t=a+bx_ + cx_ + \varepsilon.\, If we split our data into two groups, then we have :$$ y_t=a_1+b_1x_ + c_1x_ + \varepsilon. \, and :$$ y_t=a_2+b_2x_ + c_2x_ + \varepsilon. \, The null hypothesis of the Chow test asserts that $a\_1=a\_2$, $b\_1=b\_2$, and $c\_1=c\_2$, and there is the assumption that the model errors $\backslash varepsilon$ are independent and identically distributed from a normal distribution with unknown variance. Let $S\_C$ be the sum of squared residuals from the combined data, $S\_1$ be the sum of squared residuals from the first group, and $S\_2$ be the sum of squared residuals from the second group. $N\_1$ and $N\_2$ are the number of observations in each group and $k$ is the total number of parameters (in this case, 3). Then the Chow test statistic is :$$ \frac. The test statistic follows the F distribution with $k$ and $N\_1+N\_2-2k$ degrees of freedom. Remarks - The global sum of squares (SSE) if often called Restricted Sum of Squares (RSSM) as we basically test a constrained model where we have 2K assumptions (with K the number of regressors). - Some software like SAS will use a predictive Chow test when the size of a subsample is less than the number of regressors. ==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「Chow 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.