Tests for standardized generalized variances of multivariate normal populations of possibly different dimensions (Q1106588)

In many practical problems, one needs to compare variabilities of several multidimensional populations. The concept of standardized generalized variance (SGV) is introduced as an extension of the concept of GV. Considering multivariate normal populations of possibly different dimensions and general covariance matrices, LRTs are derived for SGVs. The criteria turn out to be elegant multivariate analogues to those for tests for variances in the univariate cases. The null and nonnull distributions of the test criteria are deduced in computable forms in terms of special functions, e.g., Pincherle's H-function, by exploiting the theory of calculus of residues [\textit{A. M. Mathai} and \textit{R. K. Saxena}, Ann. Math. Statist. 40, 1439-1448 (1969; Zbl 0186.530)].