A0638
Title: Asymptotics of tail pairwise dependence matrices
Authors: Stephane Lhaut - ENSAE Paris (France) [presenting]
Johan Segers - KU Leuven (Belgium)
Anna Kiriliouk - University of Namur (Belgium)
Abstract: In recent literature on multivariate extremes, various definitions of tail pairwise dependence matrices (TPDMs) have been proposed to summarize the tail dependence structure of a random vector X. Most of these approaches rely on the assumption that X is multivariate regularly varying, which implies that all marginal tails are equivalent. Several popular definitions of TPDMs are unified, and it is shown how nonparametric inference can be carried out in each case without requiring multivariate regular variation of X. Instead, regular variation of a standardized version V is assumed, where all margins have been transformed to a common scale, a more realistic assumption in many applications. The joint asymptotic normality of TPDM entries is established, based either on the empirical stable tail dependence function or on the empirical angular measure, depending on the setting. Applications include inference for parametric models and dimension reduction via multidimensional scaling.
