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A Note on the Comedian for Elliptical Distributions

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  • Falk, Michael
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 67 (1998)
    Issue (Month): 2 (November)
    Pages: 306-317

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    Handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:306-317

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    Keywords: median absolute deviation from the median robust measure of correlation comedian covariance; correlation coefficient bivariate normal vectors elliptical distributions;

    References

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    1. Michael Falk, 1997. "On Mad and Comedians," Annals of the Institute of Statistical Mathematics, Springer, 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. Maria Angeles Carnero Fernandez & Ana Pérez & Esther Ruiz Ortega, 2014. "Identification of asymmetric conditional heteroscedasticity in the presence of outliers," Statistics and Econometrics Working Papers ws141912, Universidad Carlos III, Departamento de Estadística y Econometría.

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