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

Abstract

Test statistics for one-sided and two-sided multivariate hypotheses for the high-dimensional two-sample problem with one unknown covariance matrix are proposed in this dissertation. The hypothesis tests considered are H0 : μ1 = μ2 versus H1 : μ1 > μ2 and H0 : μ1 = μ2 versus H1 : μ1 < μ2 for the one-sided case and H0 : μ1 = μ2 versus H1 : μ1 ≠ μ2 for the two-sided case. The tests are developed based on the idea of keeping as much information from the pooled sample covariance matrix as possible by arranging the blocks along its diagonal. The asymptotic distributions of the test statistics are derived under the null hypothesis. The performances of the proposed tests were evaluated with both equal and unequal sample sizes via a simulation study. The simulation results show that the proposed tests performed well for both equal and unequal sample sizes. An illustration of the efficacies of the proposed tests was carried out on a genetic microarray dataset.