A Note on the Comedian for Elliptical Distributions

Michael Falk

Journal of Multivariate Analysis, 1998, vol. 67, issue 2, 306-317

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.

Keywords: median absolute deviation from the median robust measure of correlation comedian covariance; correlation coefficient bivariate normal vectors elliptical distributions (search for similar items in EconPapers)
Date: 1998
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