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Distribution-free test for symmetry based on Bonferroni's measure

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  • Antonietta Mira

Abstract

We propose a test based on Bonferroni's measure of skewness. The test detects the asymmetry of a distribution function about an unknown median. We study the asymptotic distribution of the given test statistic and provide a consistent estimate of its variance. The asymptotic relative efficiency of the proposed test is computed along with Monte Carlo estimates of its power. This allows us to perform a comparison of the test based on Bonferroni's measure with other tests for symmetry.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:8:p:959-972
    DOI: 10.1080/02664769921963
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    References listed on IDEAS

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    1. Modarres, Reza & Gastwirth, Joseph L., 1996. "A modified runs test for symmetry," Statistics & Probability Letters, Elsevier, vol. 31(2), pages 107-112, December.
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    Cited by:

    1. Ekström, Magnus & Jammalamadaka, Sreenivasa Rao, 2012. "A general measure of skewness," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1559-1568.
    2. Laïb Naâmane & Lemdani Mohamed & Ould Saïd Elias, 2013. "A functional conditional symmetry test for a GARCH-SM model: Power asymptotic properties," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 75-104, March.
    3. Lijia Tan & Lijia Wei, 2014. "Special Section: Experiments on Learning, Methods, and Voting," Pacific Economic Review, Wiley Blackwell, vol. 19(3), pages 313-331, August.
    4. Iones Kelanemer Holban, 2024. "Non-Linearities in International Spillovers of the ECB$^\prime$s Monetary Policy. The Case of Non-ERM II Countries and Anti-Fragmentation Policy," Papers 2406.19938, arXiv.org, revised Jul 2024.
    5. 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.
    6. Bacci, Silvia & Bartolucci, Francesco, 2014. "Mixtures of equispaced normal distributions and their use for testing symmetry with univariate data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 262-272.
    7. 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.
    8. Terence Mills, 2001. "Business cycle asymmetry and duration dependence: An international perspective," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(6), pages 713-724.
    9. Víctor Leiva & Jimmy Corzo & Myrian E. Vergara & Raydonal Ospina & Cecilia Castro, 2024. "A Statistical Methodology for Evaluating Asymmetry after Normalization with Application to Genomic Data," Stats, MDPI, vol. 7(3), pages 1-17, September.
    10. Ivanović, Blagoje & Milošević, Bojana & Obradović, Marko, 2020. "Comparison of symmetry tests against some skew-symmetric alternatives in i.i.d. and non-i.i.d. setting," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).

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