Testing the equality of mean vectors for paired doubly multivariate observations in blocked compound symmetric covariance matrix setup

In this article we develop a test statistic for testing the equality of mean vectors for paired doubly multivariate observations with qq response variables and uu sites in blocked compound symmetric covariance matrix setting. We obtain a natural extension of the Hotelling’s T2T2 statistic, the Block T2T2 (BT2BT2) statistic, a convolution of two T2T2’s, which uses unbiased estimates of the component matrices of the orthogonally transformed blocked compound symmetric covariance matrix that is present in a data set. The new test statistic is implemented with two real data sets. We compare our findings with the conventional Hotelling’s T2T2 statistic.