✦ LIBER ✦

A Note on the Comedian for Elliptical Distributions

✍ Scribed by Michael Falk

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 228 KB
Volume: 67
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.1998.1775

No coin nor oath required. For personal study only.

✦ Synopsis

The comedian COM(X, Y) of random variables X, Y is a median based robust alternative to the covariance of X of Y. For the bivariate normal case it is known that COM(X, Y ), standardized by the median absolute deviations of X and Y, is a symmetric, strictly increasing and continuous function of the correlation coefficient \ with range [&1, 1] and can therefore serve as a robust alternative to . We show that this result, which is not true in general, extends to elliptical distributions even in the case where moments of X, Y do not exist.

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