翻訳と辞書 Words near each other ・ "O" Is for Outlaw ・ "O"-Jung.Ban.Hap. ・ "Ode-to-Napoleon" hexachord ・ "Oh Yeah!" Live ・ "Our Contemporary" regional art exhibition (Leningrad, 1975) ・ "P" Is for Peril ・ "Pimpernel" Smith ・ "Polish death camp" controversy ・ "Pro knigi" ("About books") ・ "Prosopa" Greek Television Awards ・ "Pussy Cats" Starring the Walkmen ・ "Q" Is for Quarry ・ "R" Is for Ricochet ・ "R" The King (2016 film) ・ "Rags" Ragland ・ ! (album) ・ ! (disambiguation) ・ !! ・ !!! ・ !!! (album) ・ !!Destroy-Oh-Boy!! ・ !Action Pact! ・ !Arriba! La Pachanga ・ !Hero ・ !Hero (album) ・ !Kung language ・ !Oka Tokat ・ !PAUS3 ・ !T.O.O.H.! ・ !Women Art Revolution 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 Cook–Weisberg test ： ウィキペディア英語版 Breusch–Pagan test In statistics, the Breusch–Pagan test, developed in 1979 by Trevor Breusch and Adrian Pagan, is used to test for heteroskedasticity in a linear regression model. It was independently suggested with some extension by R. Dennis Cook and Sanford Weisberg in 1983. It tests whether the estimated variance of the residuals from a regression are dependent on the values of the independent variables. In that case, heteroskedasticity is present. Suppose that we estimate the regression model :$$ y = \beta_0 + \beta_1 x + u, \, and obtain from this fitted model a set of values for $\backslash hat$, the residuals. Ordinary least squares constrains these so that their mean is 0 and so, given the assumption that their variance does not depend on the independent variables, an estimate of this variance can be obtained from the average of the squared values of the residuals. If the assumption is not held to be true, a simple model might be that the variance is linearly related to independent variables. Such a model can be examined by regressing the squared residuals on the independent variables, using an auxiliary regression equation of the form :$$ \hat^2 = \gamma_0 + \gamma_1 x + v.\, This is the basis of the Breusch–Pagan test. If an F-test confirms that the independent variables are jointly significant then the null hypothesis of homoskedasticity can be rejected. The Breusch–Pagan test tests for conditional heteroskedasticity. It is a chi-squared test: the test statistic is ''n''χ2 with ''k'' degrees of freedom. It tests the null hypothesis of homoskedasticity. If the Chi Squared value is significant with p-value below an appropriate threshold (e.g. p<0.05) then the null hypothesis of homoskedasticity is rejected and heteroskedasticity assumed. If the Breusch–Pagan test shows that there is conditional heteroskedasticity, the original regression can be corrected by using the Hansen method, using robust standard errors, or re-thinking the regression equation by changing and/or transforming independent variables. ==Procedure== Under the classical assumptions, ordinary least squares is the best linear unbiased estimator (BLUE), i.e., it is unbiased and efficient. It remains unbiased under heteroskedasticity, but efficiency is lost. Before deciding upon an estimation method, one may conduct the Breusch–Pagan test to examine the presence of heteroskedasticity. The Breusch–Pagan test is based on models of the type $\backslash sigma\_i^2\; =\; h(z\_i\text{'}\backslash gamma)$ for the variances of the observations where $z\_i\; =\; (1,\; z\_,\; \backslash dots,\; z\_)$ explain the difference in the variances. The null hypothesis is equivalent to the $(p\; -\; 1)\backslash ,$ parameter restrictions: :$$ \gamma_2 = \dots = \gamma_p = 0. The following Lagrange multiplier (LM) yields the test statistic for the Breusch–Pagan test: :$$ LM=\left (\frac \right )'\left (-E\left (asymptotically distributed as $\backslash chi^2\_$ under the null hypothesis of homoskedasticity. 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「Breusch–Pagan 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.