Abstract: This study aims to develop homogeneity tests for high-dimensional mean vectors and covariance matrices, in which the number of features may be greater than the sample size. We introduce two categorically weighted statistics to test the equality of means and of covariance matrices. We establish the asymptotic distributions of the proposed test statistics under certain mild conditions, and develop simplified algorithms to facilitate the implementation and application. Simulation studies demonstrate the satisfactory performance of the proposed tests in terms of the empirical size and power. We also apply the proposed test procedures to two microarray data sets.

Key words and phrases: High-dimension, homogeneity, K-sample problem, location and scale, MANOVA.