Paper detail

Statistical applications of Random matrix theory: comparison of two populations II

This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is, the number of variables. Inspired by the spike models used in random matrix theory, we concentrate on the largest eigenvalues of the matrices in order to determine significance. To avoid false rejections we must guard against residual spikes and need a sufficiently precise description of the behaviour of the largest eigenvalues under the null hypothesis. In this paper we propose some "invariant" theorems that allows us to extend the test of arXiv:2002.12741 for perturbation of order $1$ to some general tests for order $k$. The statistics introduced in this paper allow the user to test the equality of two populations based on high-dimensional multivariate data. Simulations show that these tests have more power of detection than standard multivariate approaches.