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A Treatment of Multivariate Skewness, Kurtosis, and Related Statistics

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  • Klar, Bernhard

Abstract

This paper gives a unified treatment of the limit laws of different measures of multivariate skewness and kurtosis which are related to components of Neyman's smooth test of fit for multivariate normality. The results are also applied to other multivariate statistics which are built up in a similar way as the smooth components. Special emphasis is given to the case that the underlying distribution is elliptically symmetric.

Suggested Citation

  • Klar, Bernhard, 2002. "A Treatment of Multivariate Skewness, Kurtosis, and Related Statistics," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 141-165, October.
    • Handle: RePEc:eee:jmvana:v:83:y:2002:i:1:p:141-165
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    References listed on IDEAS

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    1. Gutjahr, Steffen & Henze, Norbert & Folkers, Martin, 1999. "Shortcomings of Generalized Affine Invariant Skewness Measures," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 1-23, October.
    2. Henze, Norbert, 1997. "Limit laws for multivariate skewness in the sense of Móri, Rohatgi and Székely," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 299-307, May.
    3. J. Koziol, 1987. "An alternative formulation of Neyman’s smooth goodness of fit tests under composite alternatives," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 34(1), pages 17-24, December.
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    Cited by:

    1. Kollo, Tõnu, 2008. "Multivariate skewness and kurtosis measures with an application in ICA," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2328-2338, November.
    2. Loperfido, Nicola, 2020. "Some remarks on Koziol’s kurtosis," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    3. Tanya Araujo & João Dias & Samuel Eleutério & Francisco Louçã, 2012. "How Fama Went Wrong: Measures of Multivariate Kurtosis for the Identification of the Dynamics of a N-Dimensional Market," Working Papers Department of Economics 2012/21, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    4. 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.
    5. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & György H. Terdik, 2021. "Asymptotic theory for statistics based on cumulant vectors with applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 708-728, June.
    6. Tanya Ara'ujo & Jo~ao Dias & Samuel Eleut'erio & Francisco Louc{c}~a, 2012. "How Fama Went Wrong: Measures of Multivariate Kurtosis for the Identification of the Dynamics of a N-Dimensional Market," Papers 1207.1202, arXiv.org.
    7. Yanagihara, Hirokazu, 2007. "A family of estimators for multivariate kurtosis in a nonnormal linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 1-29, January.
    8. Arismendi, Juan C. & Broda, Simon, 2017. "Multivariate elliptical truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 29-44.
    9. Margus Pihlak, 2014. "Modelling of Skewness Measure Distribution," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 15(1), pages 145-152, January.
    10. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & Gyorgy H. Terdik, 2021. "On Multivariate Skewness and Kurtosis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 607-644, August.
    11. Arismendi, J.C., 2013. "Multivariate truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 41-75.

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