The classical theory for testing the null hypothesis that a set of canonical correlation coefficients is zero leads to a chi-square test under the assumption of multi-normality. The test has been used in the context of dimension reduction. In this paper, we study the limiting distribution of the test statistic without the normality assumption, and obtain a necessary and sufficient condition for the chi-square limiting distribution to hold. Implications of the result are also discussed for the problem of dimension reduction. © 2003 Elsevier Science (USA). All rights reserved.
Bai, Z. D., & He, X. (2004). A chi-square test for dimensionality with non-Gaussian data. Journal of Multivariate Analysis, 88(1), 109–117. https://doi.org/10.1016/S0047-259X(03)00056-3