• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.501-510
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• 2020

Mardia (Biometrika, 57, 519-530, 1970) defined measures of multivariate skewness and kurtosis. Based on these measures, omnibus test statistics of multivariate normality are proposed using normalizing transformations. The transformations we consider are normal approximation and a Wilson-Hilferty transformation. The normalizing transformation proposed by Enomoto et al. (Communications in Statistics-Simulation and Computation, 49, 684-698, 2019) for the Mardia's kurtosis is also considered. A comparison of power is conducted by a simulation study. As a result, sum of squares of the normal approximation to the Mardia's skewness and the Enomoto's normalizing transformation to the Mardia's kurtosis seems to have relatively good power over the alternatives that are considered.

• The Korean Journal of Applied Statistics
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• v.17 no.3
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• pp.507-518
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• 2004

Malkovich & Afifi (1973) generalized the univariate skewness and kurtosis to test a hypothesis of multivariate normality by use of the union-intersection principle. However these statistics are hard to compute for high dimensions. We propose the approximate statistics to them, which are practical for a high dimensional data set. We also compare the proposed statistics to Mardia(1970)'s multivariate skewness and kurtosis by a Monte Carlo study.