Approximate Power Functions for Some Robust Tests of Regression Coefficients.

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.