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A Note on the Comedian for Elliptical Distributions

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  • Falk, Michael

Abstract

The comedianCOM(X, Y) of random variablesX,Yis a median based robust alternative to the covariance ofXofY. For the bivariate normal case it is known thatCOM(X, Y), standardized by the median absolute deviations ofXandY, is a symmetric, strictly increasing and continuous function of the correlation coefficient[rho]with range [-1, 1] and can therefore serve as a robust alternative to[rho]. We show that this result, which is not true in general, extends to elliptical distributions even in the case where moments ofX,Ydo not exist.

Suggested Citation

  • Falk, Michael, 1998. "A Note on the Comedian for Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 306-317, November.
    • Handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:306-317
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    References listed on IDEAS

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    1. Michael Falk, 1997. "On Mad and Comedians," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(4), pages 615-644, December.
    2. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Cited by:

    1. M. Angeles Carnero & Ana Pérez & Esther Ruiz, 2016. "Identification of asymmetric conditional heteroscedasticity in the presence of outliers," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 179-201, March.
    2. repec:cte:wsrepe:es142416 is not listed on IDEAS
    3. Christophe Croux & Catherine Dehon, 2008. "Robustness versus Efficiency for Nonparametric Correlation Measures," Working Papers ECARES 2008_002, ULB -- Universite Libre de Bruxelles.
    4. Gareth W. Peters & Matteo Malavasi & Georgy Sofronov & Pavel V. Shevchenko & Stefan Trück & Jiwook Jang, 2023. "Cyber loss model risk translates to premium mispricing and risk sensitivity," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(2), pages 372-433, April.
    5. Christophe Croux & Catherine Dehon, 2010. "Influence functions of the Spearman and Kendall correlation measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 497-515, November.
    6. Harry-Paul Vander Elst & David Veredas, 2014. "Disentangled Jump-Robust Realized Covariances and Correlations with Non-Synchronous Prices," Working Papers ECARES ECARES 2014-35, ULB -- Universite Libre de Bruxelles.
    7. Gareth W. Peters & Matteo Malavasi & Georgy Sofronov & Pavel V. Shevchenko & Stefan Truck & Jiwook Jang, 2022. "Cyber Loss Model Risk Translates to Premium Mispricing and Risk Sensitivity," Papers 2202.10588, arXiv.org, revised Mar 2023.

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