Abstract
In this paper we consider the usual test statistics for dimensionality in canonical correlation and MANOVA models for nonnormal populations. In order to know the effects of the null distributions of the test statistics when the populations depart from normality, perturbation expansions for test statistics are derived. The asymptotic expansions of the expectations of the test statistics are given under the class of elliptical populations. Further, modified test statistics with a better chi-squared approximation are proposed. Finally, numerical results by Monte Carlo simulations are presented.
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