On the Optimality of Some Tests of the Error Covariance Matrix in the Linear Regression Model
本文采用条件分布方法，证明了线性回归模型中误差协方差矩阵的点最优检验是最优的，并提出了渐近最优检验准则，指出双边Durbin-Watson检验和拉格朗日乘子检验分别对序列相关和异方差扰动是渐近最优的。
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.