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In this paper, we propose a new test for linear hypothesis of  k -sample mean vectors in high-dimensional normal models based on generalized likelihood ratio method. The proposed test is designed for the “large  p  small  n ” situation where the data dimension  p  is much larger than the sample size  n . The asymptotic null and non null distributions of the proposed test are derived under mild conditions. Simulation results show that our new test outperforms some competitors in both size and power. Moreover, our new test can also be applied to non normal data.

A generalized likelihood ratio test for linear hypothesis of k -sample means in high dimension