  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 problem in multivariate statistical analysis and there have
been various tests proposed in the literature. Motivated by \citet{BaiS96E} and
\cite{ChenQ10T}, a test statistic is introduced and the asymptomatic
distributions under the null hypothesis as well as the alternative hypothesis
are given. In addition, it is compared with a test statistic recently proposed
by \cite{SrivastavaK13Ta}. It is shown that our test statistic performs much
better especially in the large dimensional case.
