AN IMPROVEMENT OF MULTIVARIATE JB TYPE TEST STATISTIC BY NORMALIZING TRANSFORMATION

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  • Sumikawa Takuma
    Dept. of Mathematical Information Science, Graduate School of Science, Tokyo University of Science
  • Koizumi Kazuyuki
    Dept. of International College of Arts and Sciences, Yokohama City University
  • Seo Takashi
    Dept. of Mathematical Information Science, Faculty of Science, Tokyo University of Science

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  • 正規化変換を用いた総括的な多変量正規性検定統計量の改良
  • セイキカ ヘンカン オ モチイタ ソウカツテキ ナ タヘンリョウ セイキセイ ケンテイ トウケイリョウ ノ カイリョウ

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Abstract

In this paper, 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 e.g. Mardia (1970) and Srivastava (1984), were then extended by Koizumi et al. (2009) who proposed the multivariate Jarque-Bera type test (MJB_1) based on the Srivastava's (1984) principal components measure scores of skewness and kurtosis. We consider an improved MJB test (MJB_2) which is based on Cornish-Fisher expansion. We propose an MJB type of test (cMJB) corrected asymptotic bias of MJB_2 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 MJB_1 and MJB_2 for a number of high-dimensional scenarios.

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