On the Optimality of Some Tests of the Error Covariance Matrix in the Linear Regression Model

SUMMARY

This paper adopts the approach of conditional distributions to investigate the optimality of some tests of the error covariance matrix in the linear regression model. Specifically, we show that point optimal tests, advocated by King and Evans and King, are the most powerful similar test. We also derive the locally best similar and the locally best unbiased similar tests. Finding the latter cumbersome to apply, we then propose the asymptotically best similar and the asymptotically best unbiased similar (ABUS) tests as alternative criteria. We show that the two‐sided Durbin–Watson test is ABUS against serial correlation and that the two‐sided Lagrange multiplier test is ABUS against heteroscedastic disturbances.