On the Non-degeneracy of Kendall's and Spearman's Correlation Coefficients

Details On the Non-degeneracy of Kendall's and Spearman's Correlation Coefficients On the Non-degeneracy of Kendall's and Spearman's Correlation Coefficients

2007-11-21

arxiv.org/abs/0711.3400v2

Mathematics

Statistics Theory

4 pages; to the statements in version 1 on Kendall's correlation statistic now added quite similar statements on Spearman's on

Scientific paper

Hoeffding proved that Kendall's and Spearman's nonparametric measures of correlation between two continuous random variables X and Y are each asymptotically normal with an asymptotic variance of the form sigma^2/n -- provided the non-degeneracy condition sigma^2>0 holds, where sigma^2 is a certain (always nonnegative) expression which is determined by the joint distribution (say mu) of X and Y. Sufficient conditions for sigma^2>0 in terms of the support set (say S) of mu are given, the same for both correlation statistics. One of them is that there exist a rectangle with all its vertices in S, sides parallel to the X and Y axes, and an interior point also in S. Another sufficient condition is that the Lebesgue measure of S be nonzero.

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