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Computational Statistics

, Volume 17, Issue 1, pp 117–122 | Cite as

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

  • Douglas G. Bonett
  • J. Arthur Woodward
  • Robert L. Randall
Article

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.

Keywords

Kurtosis Monte Carlo Multivariate normality p-value Skewness 

References

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  2. D’Agostino, R.B. & Stephens, M.A. (1986), Goodness-of-fit Techniques. Marcel Dekker, New York.zbMATHGoogle Scholar
  3. Mardia, K.V.(1970), Measures of multivariate skewness and kurtosis with applications, Biometrika, 57, 519–530.MathSciNetCrossRefGoogle Scholar
  4. Mardia, K.V. (1974), Applications of some measures of multivariate skewness and kurtosis for testing normality and robustness studies,” Sankhya B, 36, 115–128.MathSciNetzbMATHGoogle Scholar
  5. Rencher, A.C. (1995), Methods of Multivariate Analysis. Wiley, New York.zbMATHGoogle Scholar
  6. Seber, G.A.F. (1984), Multivariate Observations. Wiley, New York.CrossRefGoogle Scholar

Copyright information

© Physica-Verlag 2002

Authors and Affiliations

  • Douglas G. Bonett
    • 1
  • J. Arthur Woodward
    • 2
  • Robert L. Randall
    • 3
  1. 1.Department of StatisticsIowa State UniversityAmesUSA
  2. 2.Departments of Psychology and StatisticsUCLALos AngelesUSA
  3. 3.Department of PsychologyUniversity of HawaiiHonoluluUSA

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