The Effects of Nonnormality of Tests for Dimensionality in Canonical Correlation and MANOVA Models

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 stat...

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Bibliographic Details
Published in:Journal of multivariate analysis 1995-02, Vol.52 (2), p.325-337
Main Authors: Seo, T., Kanda, T., Fujikoshi, Y.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematics
Multivariate analysis
Probability and statistics
Sciences and techniques of general use
Statistics
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Summary: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.
ISSN:0047-259X
1095-7243
DOI:10.1006/jmva.1995.1017