A new test for multivariate normality

Authors:
Gábor J. Székely;Maria L. Rizzo
Affiliations:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH;Department of Mathematics, Ohio University, Athens, OH
Venue:
Journal of Multivariate Analysis
Year:
2005

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Abstract

We propose a new class of rotation invariant and consistent goodness-of-fit tests for multivariate distributions based on Euclidean distance between sample elements. The proposed test applies to any multivariate distribution with finite second moments. In this article we apply the new method for testing multivariate normality when parameters are estimated. The resulting test is affine invariant and consistent against all fixed alternatives. A comparative Monte Carlo study suggests that our test is a powerful competitor to existing tests, and is very sensitive against heavy tailed alternatives.