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On assessing multivariate normality based on shapiro-wilk W statistic

Author

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  • Srivastava, M. S.
  • Hui, T. K.

Abstract

Shapiro and Wilk's (1965) W statistic has been found to be the best omnibus test for detecting departures from univariate normality. Royston (1983) extends the application of W to testing multivariate normality but the procedure involves a certain approximation which needs to be justified. The procedures proposed in the present paper do not need such an approximation. The asymptotic null distributions are also given. Finally, a numerical example is used to illustrate the procedures.

Suggested Citation

  • Srivastava, M. S. & Hui, T. K., 1987. "On assessing multivariate normality based on shapiro-wilk W statistic," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 15-18, January.
    • Handle: RePEc:eee:stapro:v:5:y:1987:i:1:p:15-18
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    Citations

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    Cited by:

    1. Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
    2. Liang, Jiajuan & Tang, Man-Lai & Chan, Ping Shing, 2009. "A generalized Shapiro-Wilk W statistic for testing high-dimensional normality," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3883-3891, September.
    3. Diego Norena-Chavez & Ruben Guevara, 2020. "Entrepreneurial Passion and Self-Efficacy as Factors Explaining Innovative Behavior: A Mediation Model," International Journal of Economics & Business Administration (IJEBA), International Journal of Economics & Business Administration (IJEBA), vol. 0(3), pages 352-373.
    4. Rebba, Ramesh & Mahadevan, Sankaran, 2006. "Validation of models with multivariate output," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 861-871.
    5. Sándor Csörgő, 1989. "Consistency of some tests for multivariate normality," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 107-116, December.
    6. Bruno Ebner & Norbert Henze, 2020. "Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 845-892, December.
    7. Kim, Namhyun, 2016. "A robustified Jarque–Bera test for multivariate normality," Economics Letters, Elsevier, vol. 140(C), pages 48-52.

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