A tail-sensitive generalization of Spearman’s coefficient for upper-tail dependence analysis
In this paper, we introduce two classes of copula-based dependence measures designed to assess tail dependence at sub-asymptotic levels. The first class includes, as special cases, Spearman’s coefficient and Blest’s index, while the second arises as a limiting case of the first. Our approach generalizes Spearman’s coefficient to focus explicitly on tail behavior, offering a flexible and interpretable tool for evaluating co-movements in extreme, yet non-asymptotic, regions of the distribution. For both classes, we establish theoretical properties, propose rank-based estimators, derive their asymptotic distributions, and demonstrate their performance through simulation studies and an empirical application.
Keywords: Tail dependence Order statistics Concomitants