  Motivated by the likelihood ratio test under the Gaussian assumption, we
develop a maximum sum-of-squares test for conducting hypothesis testing on high
dimensional mean vector. The proposed test which incorporates the dependence
among the variables is designed to ease the computational burden and to
maximize the asymptotic power in the likelihood ratio test. A simulation-based
approach is developed to approximate the sampling distribution of the test
statistic. The validity of the testing procedure is justified under both the
null and alternative hypotheses. We further extend the main results to the two
sample problem without the equal covariance assumption. Numerical results
suggest that the proposed test can be more powerful than some existing
alternatives.
