Asymptotic Distributions of Some Multivariate Tests

Abstract

In this paper it is shown how the systems of partial differential equations developed by the author [15] for the hypergeometric functions of matrix argument may be used to obtain asymptotic expansions for some distributions occurring in multivariate analysis. In particular expansions are derived for the distributions of Hotelling's generalized $T_0^2$-statistic, Pillai's $V^{(s)}$ criterion, and the largest latent root of the sample covariance matrix.