Two-Sample High Dimensional Mean Test Based On Prepivots

Abstract: Testing equality of mean vectors is a very commonly used criterion when comparing two multivariate random variables. Traditional tests such as Hotelling's T-squared become either unusable or output small power when the number of variables is greater than the combined sample size. In this paper, w}e propose a test using both prepivoting and Edgeworth expansion for testing the equality of two population mean vectors in the "large p, small n" setting. The asymptotic null distribution of the test statistic is derived and it is shown that the power of suggested test converges to one under certain alternatives when both n and p increase to infinity against sparse alternatives. Finite sample performance of the proposed test statistic is compared with other recently developed tests designed to also handle the "large p, small n" situation through simulations. The proposed test achieves competitive rates for both type I error rate and power. The usefulness of our test is illustrated by applications to two microarray gene expression data sets