On testing the equality of mean vectors in high dimension

Abstract

In this article, we review various tests that have been proposed in the literature for testing the equality of several mean vectors. In particular, it includes testing the equality of two mean vectors, the so-called two-sample problem as well as that of testing the equality of several mean vectors, the so-called multivariate analysis of variance or MANOVA problem. The total sample size, however, may be less than the dimension of the mean vectors, and so usual tests cannot be used. Powers of these tests are compared using simulation.