A0873
Title: Extremes in high dimensions: Methods and scalable algorithms
Authors: Marco Oesting - University of Stuttgart (Germany) [presenting]
Johannes Lederer - Ruhr-University Bochum (Germany)
Abstract: The extreme-value theory has been explored in considerable detail for univariate and low-dimensional observations, but the field is still in an early stage regarding high-dimensional multivariate observations. The method focuses on Huesler-Reiss models and their domain of attraction, a popular class of models for multivariate extremes that exhibit similarities to multivariate Gaussian distributions. Novel estimators are devised for the parameters of this model based on score matching and equip these estimators with state-of-the-art theories for high-dimensional settings and exceptionally scalable algorithms. A simulation study is performed to 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 that can be fitted within a couple of minutes on a standard laptop. A real data example on weather extremes illustrates their usefulness for applications.
