Tail-weighted dependence measures with limit being the tail dependence coefficient

Abstract

For bivariate continuous data, measures of monotonic dependence are based on the rank transformations of the two variables. For bivariate extreme value copulas, there is a family of estimators (Formula presented.), for α> 0, of the extremal coefficient, based on a transform of the absolute difference of the α power of the ranks. In the case of general bivariate copulas, we obtain the probability limit ζα of (Formula presented.) as the sample size goes to infinity and show that (i) ζα for (Formula presented.) is a measure of central dependence with properties similar to Kendall's tau and Spearman's rank correlation, (ii) ζα is a tail-weighted dependence measure for large α, and (iii) the limi..