Two-sample multivariate tests for high-dimensional data when one covariance matrix is unknown

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In this study, the test statistics for one-sided and two-sided multivariate hypotheses to the high-dimensional two-sample problem with one unknown covariance matrix were proposed. The tests were developed based on the idea of keeping as much information as possible from the pooled sample covariance matrix by arranging the blocks along its diagonal. The asymptotic distributions of the test statistics were derived under the null hypothesis. The performance of the proposed tests were evaluated on both equal and unequal sample sizes via a simulation study. The simulated results showed that the proposed tests performed well for both equal and unequal sample sizes. An illustration of the proposed tests was carried out using a dataset of prostate cancer microarray.