Tests for multivariate normality based on canonical correlations

TL;DR

This paper introduces new affine invariant tests for multivariate normality using canonical correlations of sample moments, showing higher power than existing tests in simulations.

Contribution

It presents a novel class of tests based on canonical correlations, generalizing previous methods and demonstrating improved performance.

Findings

New tests outperform traditional methods in power

Tests are affine invariant and based on sample moments

Simulation studies confirm higher detection ability

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.