B1133
Title: Extremes in high dimensions: Methods and scalable algorithms
Authors: Marco Oesting - University of Stuttgart (Germany) [presenting]
Johannes Lederer - Ruhr-University Bochum (Germany)
Abstract: Extreme value theory for univariate and low-dimensional observations has been explored in considerable detail, but the field is still in an early stage regarding high-dimensional settings. The focus is on a popular class of models for multivariate extremes similar to multivariate Gaussian distributions, the Huesler-Reiss models, and their domain of attraction. Novel estimators are devised for the model parameters based on score matching, and the estimators are equipped with state-of-the-art theories and exceptionally scalable algorithms. Simulations and applications to weather extremes demonstrate that the estimators can estimate a large number of parameters reliably and fast; for example, Huesler-Reiss models with thousands of parameters are shown to be fitted within a couple of minutes on a standard laptop. More generally speaking, the work relates extreme value theory to modern high-dimensional statistics and convex optimization concepts.
