Inference on mean sub-vectors of two multivariate normal populations with unequal covariance matrices

The problem of testing the equality of sub-vectors of two multivariate normal mean vectors is addressed when the complementary sub-vectors are known to be equal, and the two populations have unequal covariance matrices. A test procedure is derived using the multivariate Satterthwaite approximation. The approximation is developed in such a way that the test satisfies a natural invariance condition. Accuracy of the approximation is numerically investigated, and the result is illustrated with an example.