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Simultaneous hypotheses testing in models with blocked compound symmetric covariance structure

Abstract In this article, authors consider simultaneous testing hypotheses about structure of mean vector and covariance matrix in models with some special covariance structure, so-called blocked compound symmetric (BCS) covariance structure, for variate observations over u levels of some factor on each of n individual under the assumption of multivariate normality. Authors, using framework of ratio of positive and negative parts of best unbiased estimators, obtain test statistic for simultaneous test and prove that under null hypothesis the statistic has exact F distribution. Simulation study is conducted to show strong and weak sides of considered test which is compared with two other F tests for testing single hypotheses about mean and covariance matrix.