Omnibus tests for multivariate normality based on Mardia’s skewness and kurtosis using normalizing transformation

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 aWilson-Hilferty tran...

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Bibliographic Details
Published inCommunications for statistical applications and methods Vol. 27; no. 5; pp. 501 - 510
Main Author Kim, Namhyun
Format Journal Article
LanguageKorean
Published 한국통계학회 30.09.2020
Subjects
goodness-of-fit test
Mardia’s kurtosis
Mardia’s skewness
multivariate normality
power comparison
multivariate normality
goodness-of-fit test
Mardia's kurtosis
Mardia's skewness
power comparison
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Summary: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 aWilson-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.
Bibliography:The Korean Statistical Society
KISTI1.1003/JNL.JAKO202033564390394
ISSN:2287-7843