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Likelihood ratio tests for multivariate normality

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  • Ilmun Kim
  • Sangun Park

Abstract

This paper presents some powerful omnibus tests for multivariate normality based on the likelihood ratio and the characterizations of the multivariate normal distribution. The power of the proposed tests is studied against various alternatives via Monte Carlo simulations. Simulation studies show our tests compare well with other powerful tests including multivariate versions of the Shapiro–Wilk test and the Anderson–Darling test.

Suggested Citation

  • Ilmun Kim & Sangun Park, 2018. "Likelihood ratio tests for multivariate normality," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(8), pages 1923-1934, April.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:8:p:1923-1934
    DOI: 10.1080/03610926.2017.1332218
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    Cited by:

    1. Wanfang Chen & Marc G. Genton, 2023. "Are You All Normal? It Depends!," International Statistical Review, International Statistical Institute, vol. 91(1), pages 114-139, April.
    2. Sirao Wang & Jiajuan Liang & Min Zhou & Huajun Ye, 2022. "Testing Multivariate Normality Based on F -Representative Points," Mathematics, MDPI, vol. 10(22), pages 1-22, November.
    3. Vexler, Albert, 2020. "Univariate likelihood projections and characterizations of the multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    4. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "Testing multivariate normality by zeros of the harmonic oscillator in characteristic function spaces," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 456-501, June.

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