Limiting behavior of eigenvalues in high-dimensional MANOVA via RMT

Abstract

In this paper, we derive the asymptotic joint distributions of the eigenvalues under the null case and the local alternative cases in the MANOVA model and multiple discriminant analysis when both the dimension and the sample size are large. Our results are obtained by random matrix theory (RMT) without assuming normality in the populations. It is worth pointing out that the null and nonnull distributions of the eigenvalues and invariant test statistics are asymptotically robust against departure from normality in high-dimensional situations. Similar properties are pointed out for the null distributions of the invariant tests in multivariate regression model. Some new formulas in RMT are also presented.