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

Namhyun Kim | Zendy

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

Author(s) -

Namhyun Kim

Publication year - 2020

Publication title -

communications for statistical applications and methods

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.326

H-Index - 6

eISSN - 2383-4757

pISSN - 2287-7843

DOI - 10.29220/csam.2020.27.5.501

Subject(s) - kurtosis , mathematics , skewness , multivariate statistics , normality , transformation (genetics) , multivariate normal distribution , statistics , normality test , econometrics , power transform , statistical hypothesis testing , discrete mathematics , biochemistry , chemistry , consistency (knowledge bases) , gene

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.

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