Two-sample test in high dimensions through random selection

Abstract Testing the equality for two-sample means with high dimensional distributions is a fundamental problem in statistics. In the past two decades, many efforts have been devoted to comparing the mean vectors of two populations. Many existing tests rely on naive diagonal or trace estimators of the covariance matrix, ignoring the dependence structure between variables. To make more use of the dependence structure, a new nonparametric test based on random selections is proposed to test the population mean vector of nonnormal high-dimensional multivariate data. This makes more efficient use of the covariance structure to deal with dependent variables. The asymptotic null distribution of the proposed test is standard normal, regardless of the parent distributions of the random samples and the relations between data dimensions and sample sizes. Extensive simulations show that the power performance of the proposed test is encouraging compared with some existing methods.