Title: Principal component decomposition and completely positive decomposition of dependence for multivariate extremes
Authors: Emeric Thibaud - EPFL (Switzerland) [presenting]
Daniel Cooley - Colorado State University (United States)
Abstract: Multivariate regular variation is a framework which is useful for describing tail dependence and estimating probabilities of multivariate extreme events. Dependence for regularly-varying random vectors is described by the angular measure. In large dimensions, this measure is difficult to estimate. Inspired by principal component analysis (PCA) in the non-extreme setting, we propose two decompositions of a matrix which summarizes pairwise tail dependence in a regularly-varying random vector. The first decomposition is useful to understand the largest modes of dependence as is done with traditional PCA. The second decomposition is useful for calculating probabilities of extreme regions and for simulation. We illustrate methods with an application to daily precipitation measurements at 44 stations in Switzerland.