Title: A unified approach for tail-dependence and concordance measures, with some new indices
Authors: Claudio Giovanni Borroni - University of Milano - Bicocca (Italy) [presenting]
Lucio De Capitani - University of Milano - Bicocca (Italy)
Abstract: Some applications need indices measuring the limiting amount of dependence in the upper and lower corners of a copula. Classical Sibuya's tail-dependence coefficient is based on the limit of the diagonal section of the copula, something which is often regarded as too restrictive, because the index does not account for dependence along routes to the corners other than the main diagonal. Essentially, such a limitation can be ascribed to the link of Sibuya's coefficient to a rather elementary dependence measure, Blomqvist's beta. In the literature some attempts are then made to build other indices upon more sophisticated dependence measures, even if the choice is often more motivated by the mathematical tractability of the measure, such as for Spearman's rho, rather than by its intrinsic properties. We aim, first, at building a systematic approach to link tail-dependence indices to association measures or, more specifically, to measures of concordance. Secondly, we evaluate the use of a class of highly informative measures, which can clearly distinguish among different cases of a lack of association, independence or reflection invariance. The elements of that class, sometimes referred as mutual, include Kendall's tau other non-trivial measures. Thirdly, estimation issues are addressed.