TESTING AND ESTIMATING LOCATION VECTORS WHEN THE ERROR COVARIANCE-MATRIX IS UNKNOWN

An exact test proposed by Weerahandi (1987) for testing the equality of location vectors under heteroskedasticity is compared with a commonly-used computationally simple asymptotic test. The results from a variety of sampling experiments indicate that in most instances the nominal size of Weerahandi's test (F(W)) overstates the probability of a Type I error and the nominal size of the asymptotic test (F(A)) understates the probability of a Type I error. Consequently, without size correction, the probability of a Type II error is less for F(A) than it is for F(W). With size correction the powers of the two tests are virtually identical. Within an estimation context the risk properties of the pre-test estimators generated by F(A) and F(W) are compared, and an empirical Bayes estimator is developed within the framework of the more general seemingly unrelated regressions model. Under a squared error loss measure the empirical Bayes estimator is shown to behave in a minimax way.