Statistical Methods & Applications

, Volume 23, Issue 2, pp 189–208 | Cite as

Tests for multivariate normality based on canonical correlations

  • Måns Thulin


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 in a way that resembles the construction of Mardia’s skewness measure and generalizes the Lin–Mudholkar test for univariate 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.


Goodness-of-fit Kurtosis Multivariate normality Skewness  Test for normality 



The author wishes to thank the editor and two anonymous referees for comments that helped improve the paper, and Silvelyn Zwanzig for several helpful suggestions.

Supplementary material

10260_2013_252_MOESM1_ESM.pdf (132 kb)
Supplementary material 1 (pdf 131 KB)
10260_2013_252_MOESM2_ESM.pdf (737 kb)
Supplementary material 2 (pdf 736 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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