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Asymptotic distributions and performance of empirical skewness measures

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  • Eberl, Andreas
  • Klar, Bernhard

Abstract

A number of skewness measures have been proposed and applied to theoretical distributions. However, the corresponding empirical counterparts have been analyzed only rarely, especially with respect to their asymptotic properties and limit distributions. Six of these empirical measures are considered. After discussing some general properties, the limiting distribution for each measure is derived under weak assumptions. The performance of these estimators is analyzed in simulations using tests and the coverage probabilities of confidence intervals. A particular focus is put on the standardized central third moment as the most popular measure of skewness. Since it turns out to behave poorly, especially when sample sizes are small, the use of alternative and more suitable skewness measures is recommended. A real data application illustrates some of the findings.

Suggested Citation

  • Eberl, Andreas & Klar, Bernhard, 2020. "Asymptotic distributions and performance of empirical skewness measures," Computational Statistics & Data Analysis, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:csdana:v:146:y:2020:i:c:s016794732030030x
    DOI: 10.1016/j.csda.2020.106939
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    References listed on IDEAS

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    1. I. H. Tajuddin, 1999. "A comparison between two simple measures of skewness," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(6), pages 767-774.
    2. Cedric Flecher & Denis Allard & Philippe Naveau, 2010. "Truncated skew-normal distributions: moments, estimation by weighted moments and application to climatic data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 331-345.
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    Cited by:

    1. Chenglu Jin & Thomas Conlon & John Cotter, 2023. "Co-Skewness across Return Horizons," Journal of Financial Econometrics, Oxford University Press, vol. 21(5), pages 1483-1518.
    2. Andreas Eberl & Bernhard Klar, 2023. "Stochastic orders and measures of skewness and dispersion based on expectiles," Statistical Papers, Springer, vol. 64(2), pages 509-527, April.
    3. Andreas Eberl & Bernhard Klar, 2022. "Expectile‐based measures of skewness," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 373-399, March.

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