  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.
