Inference of multivariate dependence structures in extreme value theory

Abstract

Modelling dependence structures in high-dimensional problems of extreme events is of interest in several application areas. Current dependence models for multivariate extremes are based upon max-stable distributions and one approach is to investigate the Pickands dependence function through nonparametric estimators. In the bivariate setting, there exist several estimators while more problematic are the assumptions that must be satisfied in multivariate extremes. The aim is to briefly review an existing nonparametric inference method for estimating the Pickands function, which assume known marginal distributions, in the multivariate framework.