Tests for multivariate normality based on canonical correlations

Abstract: We propose new affine invariant tests for multivariate normality, based on independence characterizations of the sample moments of the normal distribution. The test statistics are obtained using canonical correlations between sets of sample moments, generalizing the Lin-Mudholkar test for normality. The tests are compared to some popular tests based on Mardia's skewness and kurtosis measures in an extensive simulation power study and are found to offer higher power against many of the alternatives.