Locally Robust Tests for Serial Correlation in Least Squares Regression

Kariya and Eaton and Kariya studied a robustness property of the usual tests for serial correlation against departure from normality. When the results were applied to a regression model $y = X \beta + u(X: nxk),$ it was assumed that the column space of $X$ is spanned by some $k$ latent vectors of the covariance matrix of error term $u.$ In this paper we delete this assumption and in a much broader class of distributions derive a locally best invariant test for a one-sided problem and a locally best unbiased and invariant test for a two-sided problem. The null distributions of these tests are the same as those under normality.