On testing the equality of high dimensional mean vectors with unequal covariance matrices

In this article, we focus on the problem of testing the equality of several high dimensional mean vectors with unequal covariance matrices. This is one of the most important problems in multivariate statistical analysis and there have been various tests proposed in the literature. Motivated by Bai and Saranadasa (Stat Sin 6:311-329, 1996) and Chen and Qin (Ann Stat 38:808-835, 2010), we introduce a test statistic and derive the asymptotic distributions under the null and the alternative hypothesis. In addition, it is compared with a test statistic recently proposed by Srivastava and Kubokawa (J Multivar Anal 115:204-216, 2013). It is shown that our test statistic performs better especially in the large dimensional case.