Likelihood-based tests on moderate-high-dimensional mean vectors with unequal covariance matrices

This paper considers linear hypotheses of a set of high-dimensional mean vectors with unequal covariance matrices. To test the hypothesis ℋ0 : Σi=1qβiμi = μ0, we use the CLT for the linear spectral statistics of a high-dimensional F-matrix in Zheng (2012) to establish a test statistic based on the likelihood ratio test statistic that is applicable to high-dimensional non-Gaussian variables in a wide range. Furthermore, the results of a simulation are provided to compare the proposed test with other high-dimensional tests. As shown by the simulation results, the empirical size of our proposed test is closer to a significance level, whereas our empirical powers dominate those of the other tests due to the likelihood-based statistic.