Canonical Correlation: Permutation Tests and Regression Yoo, Jae-Keun; Kim, Hee-Youn; Um, Hye-Yeon;
In this paper, we present a permutation test to select the number of pairs of canonical variates in canonical correlation analysis. The existing chi-squared test is known to be limited to normality in use. We compare the existing test with the proposed permutation test and study their asymptotic behaviors through numerical studies. In addition, we connect canonical correlation analysis to regression and we we show that certain inferences in regression can be done through canonical correlation analysis. A regression analysis of real data through canonical correlation analysis is illustrated.
Canonical Correlation Analysis Through Linear Modeling, Australian & New Zealand Journal of Statistics, 2014, 56, 1, 59
Bartlett, M. S. (1938). Further aspects of the theory of multiple regression, Proceedings of the Cambridge Philosophical Society, 34, 33-40.
Bartlett, M. S. (1939). A note on tests of significance in multivariate analysis, Proceedings of the Cambridge Philosophical Society, 35, 180-185.
Breusch, T. S. and Pagan, A. R. (1979). A simple test for heteroscedasticity and random coefficient variation, Econometrika, 47, 1287-1294.
Johnson, R. A. andWichern, D.W. (2007). Applied Multivariate Statistical Analysis, 6th Ed., Pearson Prentice Hall, New Jersey.
Nierenberg,W. D., Stukel, A. T., Baron, A. J., Dain, J. B. and Greenberg, E. R. (1989). The skin cancer prevention study group, determinants of plasma levels of beta-carotene and retinol, American Journal of Epidemiology, 130, 511-521.