Distribution of the canonical correlation coefficients for the elliptical error model

In this paper it is proved that the nonnull density of the canonical correlation coefficients under the normality assumption is identical with that for the elliptical error model (EEM), thus proving the nonnull robustness of the canonical correlation coefficient density. An application of testing that the multiple correlation coefficient is zero to a result of James (1977) is also given. Further, it is shown that the results hold for any Taylor series expandable EEM density