In this article, we introduce two types of new omnibus procedures for testing multivariate normality based on the sample measures of multivariate skewness and kurtosis. These characteristics, initially introduced by, for example, Mardia (1970) and Srivastava (1984), were then extended by Koizumi, Okamoto, and Seo (2009), who proposed the multivariate Jarque-Bera type test (MJB1) based on the Srivastava (1984) principal components measure scores of skewness and kurtosis. We suggest an improved MJB test (MJB2) that is based on the Wilson-Hilferty transform, and a modified MJB test (mMJB) that is based on the F-approximation to mMJB. Asymptotic properties of both tests are examined, assuming that both dimensionality and sample size go to infinity at the same rate. Our simulation study shows that the suggested mMJB test outperforms both MJB1 and MJB2 for a number of high-dimensional scenarios. The mMJB test is then used for testing multivariate normality of the real data digitalized character image.
Jarque-Bera test Multivariate skewness Multivariate kurtosis Normality test Normalizing transformation
AMS Subject Classification: Primary
AMS Subject Classification: Secondary
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