Multivariate normality test using normalizing transformation for Mardia’s multivariate kurtosis

Abstract

Multivariate skewness and kurtosis were defined by Mardia. However, the distribution of multivariate normality test statistics based on skewness and kurtosis is only obtainable for large samples. In this paper, we propose a normalizing transformation statistic for Mardia’s multivariate kurtosis. The accuracy of the normal approximation of this statistic, i.e. its expectation, variance, skewness, kurtosis, sample error Type I, and power for chosen alternative distributions, was investigated by Monte Carlo simulations for given sizes and dimensions.

Keywords:

• Asymptotic distribution
• Asymptotic expansion
• Multivariate normal distribution
• Multivariate sample kurtosis
• Normalizing transformation

Acknowledgment

The authors are grateful to the anonymous reviewer for giving many insightful and constructive comments and suggestions, which led to the improvement of the original manuscript.