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Journal of Statistical Theory and Practice

, Volume 8, Issue 2, pp 382–399 | Cite as

Modified Jarque-Bera Type Tests for Multivariate Normality in a High-Dimensional Framework

  • Kazuyuki Koizumi
  • Masashi Hyodo
  • Tatjana Pavlenko
Article

Abstract

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.

Keywords

Jarque-Bera test Multivariate skewness Multivariate kurtosis Normality test Normalizing transformation 

AMS Subject Classification: Primary

62J15 

AMS Subject Classification: Secondary

62H15 

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Copyright information

© Grace Scientific Publishing 2014

Authors and Affiliations

  • Kazuyuki Koizumi
    • 1
  • Masashi Hyodo
    • 2
  • Tatjana Pavlenko
    • 3
  1. 1.International College of Arts and SciencesYokohama City UniversityYokohama City, KanagawaJapan
  2. 2.Graduate School of EconomicsUniversity of TokyoTokyoJapan
  3. 3.Department of MathematicsKTH Royal Institute of TechnologyStockholmSweden

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