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Approximate Power Functions for Some Robust Tests of Regression Coefficients

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Author Info
Rothenberg, Thomas J
Abstract

Edgeworth approximations are developed for the distribution functio ns of some statistics for testing a linear hypothesis on the coefficient s in a regression model with an unknown error covariance matrix. Adjust ments to the asymptotic critical values are found to insure that the tests have correct size to second order of approximation. The power loss due to the estimation of the error covariance matrix is calculated. Some examples involving heteroskedasticity and autocorrelation suggest that the null rejection probabilities of common robust regression tests are often considerably greater than their nominal level. Moreover, the cost of not knowing the error covariance matrix can be substantial. Copyright 1988 by The Econometric Society.

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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 56 (1988)
Issue (Month): 5 (September)
Pages: 997-1019
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Handle: RePEc:ecm:emetrp:v:56:y:1988:i:5:p:997-1019

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  1. Oliver Linton, 1996. "An Asymptotic Expansion in the Garch(1,1) Model," Cowles Foundation Discussion Papers 1118, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  2. Oliver Linton, 1993. "Second Order Approximation in the Partially Linear Regression Model," Cowles Foundation Discussion Papers 1065, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  3. Oliver Linton, 1997. "Second-Order Approximation for Semiparametric Instrumental Variable Estimators and Test Statistics," Cowles Foundation Discussion Papers 1151, Cowles Foundation, Yale University. [Downloadable!]
  4. Douglas Steigerwald & Jack Erb, 2007. "Accurately Sized Test Statistics with Misspecified Conditional Homoskedasticity," University of California at Santa Barbara, Economics Working Paper Series 09-07, Department of Economics, UC Santa Barbara. [Downloadable!]
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