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A general measure of skewness

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  • Ekström, Magnus
  • Jammalamadaka, Sreenivasa Rao

Abstract

A very general measure of skewness based on the quantiles is introduced, which includes several well-known measures as special cases. Sample versions of our measure may be used as test statistics for testing the hypothesis of symmetry about an unknown value. We provide large sample theory for such a statistic and discuss the asymptotic relative efficiencies of this against some competing test statistics for symmetry.

Suggested Citation

  • Ekström, Magnus & Jammalamadaka, Sreenivasa Rao, 2012. "A general measure of skewness," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1559-1568.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:8:p:1559-1568
    DOI: 10.1016/j.spl.2012.04.011
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    References listed on IDEAS

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    1. Antonietta Mira, 1999. "Distribution-free test for symmetry based on Bonferroni's measure," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 959-972.
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    Cited by:

    1. 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.
    2. Zacharias Psaradakis & Márian Vávra, 2018. "Bootstrap-Assisted Tests of Symmetry for Dependent Data," Birkbeck Working Papers in Economics and Finance 1806, Birkbeck, Department of Economics, Mathematics & Statistics.
    3. Lyubchich, Vyacheslav & Wang, Xingyu & Heyes, Andrew & Gel, Yulia R., 2016. "A distribution-free m-out-of-n bootstrap approach to testing symmetry about an unknown median," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 1-9.
    4. Herrero-Novoa, Cristina & Pérez, Isidro A. & Sánchez, M. Luisa & García, Ma Ángeles & Pardo, Nuria & Fernández-Duque, Beatriz, 2017. "Wind speed description and power density in northern Spain," Energy, Elsevier, vol. 138(C), pages 967-976.
    5. Carnero, M. Angeles & León, Angel & Ñíguez, Trino-Manuel, 2023. "Skewness in energy returns: estimation, testing and retain-->implications for tail risk," The Quarterly Review of Economics and Finance, Elsevier, vol. 90(C), pages 178-189.

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