Extremes in High Dimensions: Methods and Scalable Algorithms

Understand

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.

• This paper focuses on H\"usler-Reiss models, a popular class of models for multivariate extremes similar to multivariate Gaussian distributions, and their domain of attraction.
• We develop estimators for the model parameters based on score matching, and we equip these estimators with theories and exceptionally scalable algorithms.
• Simulations and applications to weather extremes demonstrate the fact that the estimators can estimate a large number of parameters reliably and fast; for example, we show that H\"usler-Reiss models with thousands of parameters can be fitted within a couple of minutes on a standard laptop.