Two new multivariate tests, in particular for a high dimension

Abstract

Two new test statistics for the multivariate one-sample problem are introduced that are applicable to normally distributed data in all cases with a sample size n≥2 and a dimension p≥1. The dimension may also be greater than the sample size. The tests are based on the theory of spherical distributions. They utilize the principal components of the total sums of product matrices of the given data. Under the null hypothesis, the statistics are exactly beta distributed. The performance of the tests is investigated by simulations. Finally, the methods are applied to high-dimensional data from gene expression analysis (dimension p=12625).