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Estimating p-values for Mardia’s coefficients of multivariate skewness and kurtosis

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Summary

Mardia’s coefficients of multivariate skewness and kurtosis can be used to assess the multivariate normality assumption that must be satisfied in many multivariate statistical procedures. However, the asymptotic tests of multivariate skewness and kurtosis do not perform well in small samples. A Monte Carlo method for accurately estimating the p-value is proposed and illustrated.

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References

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Author information

Authors and Affiliations

  1. Department of Statistics, Iowa State University, Ames, IA, 50011, USA

    Douglas G. Bonett

  2. Departments of Psychology and Statistics, UCLA, Los Angeles, CA, 90095-1563, USA

    J. Arthur Woodward

  3. Department of Psychology, University of Hawaii, Honolulu, HI, 96822, USA

    Robert L. Randall

Authors
  1. Douglas G. Bonett
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  2. J. Arthur Woodward
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  3. Robert L. Randall
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Appendix: Gauss program

Appendix: Gauss program

figure a

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Bonett, D.G., Woodward, J.A. & Randall, R.L. Estimating p-values for Mardia’s coefficients of multivariate skewness and kurtosis. Computational Statistics 17, 117–122 (2002). https://doi.org/10.1007/s001800200094

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  • DOI: https://doi.org/10.1007/s001800200094

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