Title: Inference methods for dependent and asymptotically independent extremes
Authors: Stefano Rizzelli - EPFL (Switzerland) [presenting]
Simone Padoan - Bocconi University (Italy)
Armelle Guillou - Strasbourg university (France)
Abstract: Inferring the dependence among extreme observations is a crucial aim of multivariate extreme-value analysis. Classical extreme-value theory provides asymptotic models for the tail probability of multivariate distributions that are in the domain of attraction of the so-called multivariate extreme value distribution. The latter is the limiting distribution of the normalized component-wise maxima. When the attractor is a product of univariate extreme value margins, a multivariate distribution is said asymptotically independent and the corresponding model for the tail probability is degenerate. In the last few decades, several characterizations of this phenomenon have emerged, and a new theory on tail probabilities has been established. Such theoretical developments are particularly useful for analyzing data that exhibit a positive association which, however, is mitigated at more and more extreme levels. Within this theoretical framework, a new dependence function is introduced which parallels the classical Pickands function but suits asymptotically independent extremes. A semi-parametric estimator of it is proposed and its asymptotic properties are established. Moreover, a statistical test for asymptotic independence is developed, which is based on the classical Pickands dependence function and suits data dimensions larger than two. The performances of the proposed inferential methods are illustrated by simulation studies.