B1189
Title: Statistical inference for Huesler-Reiss graphical models through matrix completions
Authors: Manuel Hentschel - University of Geneva (Switzerland) [presenting]
Sebastian Engelke - University of Geneva (Switzerland)
Johan Segers - Universite catholique de Louvain (Belgium)
Abstract: The dependence between the largest marginal observations drives the severity of multivariate extreme events. The Huesler-Reiss distribution is a versatile model for this extremal dependence, and a variogram matrix usually parameterizes it. To represent conditional independence relations and obtain sparse parameterizations, the novel Huesler-Reiss precision matrix is introduced. Similarly to the Gaussian case, the matrix appears naturally in density representations of the Huesler-Reiss Pareto distribution and encodes the extremal graphical structure through its zero pattern. For a given arbitrary graph, the existence and uniqueness of the completion of a partially specified Huesler-Reiss variogram matrix is proven so that its precision matrix has zeros on non-edges in the graph. Using suitable estimators for the parameters on the edges, the theory provides the first consistent estimator of graph-structured Huesler-Reiss distributions. If the graph is unknown, the method can be combined with recent structure learning algorithms to jointly infer the graph and the corresponding parameter matrix. Based on the methodology, new tools are proposed for the statistical inference of sparse Huesler-Reiss models.
