A Note on the Comedian for Elliptical Distributions
The comedianCOM(X,Â Y) of random variablesX,Yis a median based robust alternative to the covariance ofXofY. For the bivariate normal case it is known thatCOM(X,Â Y), standardized by the median absolute deviations ofXandY, is a symmetric, strictly increasing and continuous function of the correlation coefficient[rho]with range [-1,Â 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.
Volume (Year): 67 (1998)
Issue (Month): 2 (November)
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References listed on IDEAS
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- 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.
- 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.