Asymptotic Distributions in Canonical Correlation Analysis and Other Multivariate Procedures for Nonnormal Populations
Robb J. Muirhead, CHRISTINE M. WATERNAUX · Biometrika · 1980
An asymptotic theory for canonical correlation analysis is given for multivariate populations with finite fourth moments. The asymptotic distributions of the sample canonical correlation coefficients and of statistics used for testing hypotheses about the population coefficients involve the fourth order cumulants of the parent population and are sensitive to departures from normality. These asymptotic distributions have surprisingly simple forms in the case of elliptical populations; here a modified test statistic with a chi-squared approximation can be used for testing the hypothesis that some of the population coefficients are zero. Finally we note that, when sampling from elliptical populations, the asymptotic distributions of test statistics used in some other multivariate procedures are similarly simple.