Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A modified test for multivariate normality using second-power skewness and kurtosis

  • Namhyun Kim (Department of Science, Hongik University)
  • Received : 2023.02.07
  • Accepted : 2023.06.09
  • Published : 2023.07.31
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Abstract

The Jarque and Bera (1980) statistic is one of the well known statistics to test univariate normality. It is based on the sample skewness and kurtosis which are the sample standardized third and fourth moments. Desgagné and de Micheaux (2018) proposed an alternative form of the Jarque-Bera statistic based on the sample second power skewness and kurtosis. In this paper, we generalize the statistic to a multivariate version by considering some data driven directions. They are directions given by the normalized standardized scaled residuals. The statistic is a modified multivariate version of Kim (2021), where the statistic is generalized using an empirical standardization of the scaled residuals of data. A simulation study reveals that the proposed statistic shows better power when the dimension of data is big.

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Acknowledgement

This work was supported by 2022 Hongik University Research Fund.

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