Combining Independent Tests in Multivariate Linear Models

A class of independent multivariate linear models is considered, having a common parameter matrix [Theta] in their means, but having different covariance matrices. For testing H0:[Theta] = 0, some test procedures are derived, which combine the information from the different models. In the context of the interblock analysis of block designs, simulated powers of some combined tests are reported in the bivariate case, for combining the intra- and interblock tests based on the Wilk's [Lambda] criterion. The numerical results indicate that the combined tests offer substantial improvement in power compared to the Wilk's [Lambda] test based only on intrablock information.