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Measures of radial asymmetry for bivariate random vectors

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  • Azam Dehgani
  • Ali Dolati
  • Manuel Úbeda-Flores

Abstract

This article considers the problem of measuring radial asymmetry of a bivariate vector of continuous random variables whose components are symmetric about the center of symmetry. We introduce a set of axioms for measures of radial asymmetry, define new measures satisfying the axiomatic, study some properties, and present corresponding results for sample statistics. Several examples illustrate our results. Copyright Springer-Verlag 2013

Suggested Citation

  • Azam Dehgani & Ali Dolati & Manuel Úbeda-Flores, 2013. "Measures of radial asymmetry for bivariate random vectors," Statistical Papers, Springer, vol. 54(2), pages 271-286, May.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:2:p:271-286
    DOI: 10.1007/s00362-011-0425-y
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    References listed on IDEAS

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    1. Fabrizio Durante & Erich Klement & Carlo Sempi & Manuel Úbeda-Flores, 2010. "Measures of non-exchangeability for bivariate random vectors," Statistical Papers, Springer, vol. 51(3), pages 687-699, September.
    2. Nelsen, Roger B. & Molina, José Juan Quesada & Lallena, José Antonio Rodríguez & Flores, Manuel Úbeda, 2004. "Best-possible bounds on sets of bivariate distribution functions," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 348-358, August.
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    5. Fabrizio Durante, 2009. "Construction of non-exchangeable bivariate distribution functions," Statistical Papers, Springer, vol. 50(2), pages 383-391, March.
    6. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
    7. Prokhorov, Artem & Schmidt, Peter, 2009. "Likelihood-based estimation in a panel setting: Robustness, redundancy and validity of copulas," Journal of Econometrics, Elsevier, vol. 153(1), pages 93-104, November.
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    9. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 811-834, August.
    10. Fabrizio Durante & Pier Papini, 2010. "Non-exchangeability of negatively dependent random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 139-149, March.
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    Citations

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    Cited by:

    1. Monica Billio & Lorenzo Frattarolo & Dominique Guegan, 2017. "Multivariate Reflection Symmetry of Copula Functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01592147, HAL.
    2. Monica Billio & Lorenzo Frattarolo & Dominique Guégan, 2022. "High-Dimensional Radial Symmetry of Copula Functions: Multiplier Bootstrap vs. Randomization," Post-Print hal-04085236, HAL.
    3. Beare, Brendan K. & Seo, Juwon, 2020. "Randomization Tests Of Copula Symmetry," Econometric Theory, Cambridge University Press, vol. 36(6), pages 1025-1063, December.
    4. Shogo Kato & Toshinao Yoshiba & Shinto Eguchi, 2022. "Copula-based measures of asymmetry between the lower and upper tail probabilities," Statistical Papers, Springer, vol. 63(6), pages 1907-1929, December.
    5. Werner Hürlimann, 2017. "A comprehensive extension of the FGM copula," Statistical Papers, Springer, vol. 58(2), pages 373-392, June.
    6. Christian Genest & Johanna Nešlehová, 2014. "On tests of radial symmetry for bivariate copulas," Statistical Papers, Springer, vol. 55(4), pages 1107-1119, November.
    7. Billio Monica & Frattarolo Lorenzo & Guégan Dominique, 2021. "Multivariate radial symmetry of copula functions: finite sample comparison in the i.i.d case," Dependence Modeling, De Gruyter, vol. 9(1), pages 43-61, January.
    8. Pavel Krupskii, 2017. "Copula-based measures of reflection and permutation asymmetry and statistical tests," Statistical Papers, Springer, vol. 58(4), pages 1165-1187, December.
    9. Tarik Bahraoui & Nikolai Kolev, 2021. "New Measure of the Bivariate Asymmetry," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 421-448, February.

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