Extremes in High Dimensions: Methods and Scalable Algorithms

2023/03/07 by Johannes Lederer, Lederer, Johannes, Marco Oesting +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · Environmental Science · #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Hydrology and Drought Analysis

paper · pdf · doi:10.48550/arxiv.2303.04258

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. This paper focuses on Hüsler-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 Hüsler-Reiss models with thousands of parameters can be fitted within a couple of minutes on a standard laptop. More generally speaking, our work relates extreme value theory to modern concepts of high-dimensional statistics and convex optimization.

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• Ranges of Extremal Processes and Heavy-Tailed Random Walks in Spaces of Growing Dimension
• Spatial Modeling and Risk Zoning of Global Extreme Precipitation via Graph Neural Networks and r-Pareto Processes
• Clustering Tails in High Dimension

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