翻訳と辞書 Words near each other ・ Heterorhabditis bacteriophora ・ Heterorhabditis heliothidis ・ Heterorhabditis indica ・ Heterorhabditis megidis ・ Heterorhabditis zealandica ・ Heterorhachis ・ Heterorhea ・ Heterormista ・ Heterorrhina elegans ・ Heterorta ・ Heterosaccharide ・ Heterosais ・ Heterosavia ・ Heteroscarus acroptilus ・ Heteroscedasticity ・ Heteroscedasticity-consistent standard errors ・ Heteroschistis ・ Heteroscodra ・ Heteroscodra maculata ・ Heteroscodratoxin-1 ・ Heteroscorpine ・ Heteroscotia ・ Heterosemy ・ Heterosexism ・ Heterosexualism ・ Heterosexuality ・ Heterosexuals Organized for a Moral Environment ・ Heterosexual–homosexual continuum ・ Heterosigma akashiwo ・ Heterosis 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 Heteroscedasticity-consistent standard errors ： ウィキペディア英語版 Heteroscedasticity-consistent standard errors The topic of heteroscedasticity-consistent (HC) standard errors arises in statistics and econometrics in the context of linear regression as well as time series analysis. There are also known as White standard errors, Huber–White standard errors, and Eicker–Huber–White standard errors, to recognize the contributions of , Peter J. Huber, and Halbert White. In regression and time-series modelling, basic forms of models make use of the assumption that the errors or disturbances ''u''''i'' have the same variance across all observation points. When this is not the case, the errors are said to be heteroscedastic, or to have heteroscedasticity, and this behaviour will be reflected in the residuals $\backslash scriptstyle\backslash widehat$ estimated from a fitted model. Heteroscedasticity-consistent standard errors are used to allow the fitting of a model that does contain heteroscedastic residuals. The first such approach was proposed by Huber (1967), and further improved procedures have been produced since for cross-sectional data, time-series data and GARCH estimation. ==Definition== Assume that we are studying the linear regression model : $$ Y = X' \beta + U, \, where ''X'' is the vector of explanatory variables and β is a ''k'' × 1 column vector of parameters to be estimated. The ordinary least squares (OLS) estimator is : $$ \widehat \beta_ = (\mathbb' \mathbb)^ \mathbb' \mathbb. \, where $\backslash mathbb$ denotes the matrix of stacked $X\_i\text{'}$ values observed in the data. If the sample errors have equal variance σ2 and are uncorrelated, then the least-squares estimate of β is BLUE (best linear unbiased estimator), and its variance is easily estimated with : $v\_()\; =\; s^2\; (\backslash mathbb\text{'}\backslash mathbb)^,\; s^2\; =\; \backslash frac$ where $\backslash hat\; u\_i$ are regression residuals. When the assumptions of $E()\; =\; \backslash sigma^2\; I\_n$ are violated, the OLS estimator loses its desirable properties. Indeed, : $V()\; =\; V((\backslash mathbb\text{'}\backslash mathbb)^\; \backslash mathbb\text{'}\backslash mathbb)\; =\; (\backslash mathbb\text{'}\backslash mathbb)^\; \backslash mathbb\text{'}\; \backslash Sigma\; \backslash mathbb\; (\backslash mathbb\text{'}\backslash mathbb)^$ where $\backslash Sigma\; =\; V()$. While the OLS point estimator remains unbiased, it is not "best" in the sense of having minimum mean square error, and the OLS variance estimator $v\_()$ does not provide a consistent estimate of the variance of the OLS estimates. For any non-linear model (for instance Logit and Probit models), however, heteroscedasticity has more severe consequences: the maximum likelihood estimates of the parameters will be biased (in an unknown direction), as well as inconsistent (unless the likelihood function is modified to correctly take into account the precise form of heteroscedasticity). As pointed out by Greene, “simply computing a robust covariance matrix for an otherwise inconsistent estimator does not give it redemption.” 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「Heteroscedasticity-consistent standard errors」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.