Testing a block exchangeable covariance matrix

Abstract

ABSTRACTTesting hypotheses about the structure of a covariance matrix for doubly multivariate data is often considered in the literature. In this paper the Rao's score test (RST) is derived to test the block exchangeable covariance matrix or block compound symmetry (BCS) covariance structure under the assumption of multivariate normality. It is shown that the empirical distribution of the RST statistic under the null hypothesis is independent of the true values of the mean and the matrix components of a BCS structure. A significant advantage of the RST is that it can be performed for small samples, even smaller than the dimension of the data, where the likelihood ratio test (LRT) cannot be used, and it outperforms the standard LRT in a number of contexts. Simulation studies are performed for the sample size consideration, and for the estimation of the empirical quantiles of the null distribution of the test statistic. The RST procedure is illustrated on a real data set from the medical studies.