Testing linear hypotheses of mean vectors for high-dimension data with unequal covariance matrices

The asymptotic null and non-null distributions of the proposed test statistic are established in the high dimensional setting and improved estimator of the critical point of the test is derived using Cornish-Fisher expansion. As a special case, our testing procedure is applied to multivariate Behrens-Fisher problem. We illustrate the relevance and benefits of the proposed approach via Monte-Carlo simulations which show that our new test is comparable to, and in many cases is more powerful than, the tests for equality of means presented in the recent literature.