High-dimensional peaks-over-threshold inference

TL;DR

This paper introduces a score matching approach for high-dimensional peaks-over-threshold inference in extreme value processes, enabling efficient modeling of complex spatial extreme events like rainfall.

Contribution

It proposes a novel score matching method for high-dimensional extreme value models, demonstrating its effectiveness on large spatial datasets and highlighting the importance of risk choice.

Findings

Effective estimation on grids with hundreds of locations.

Successful modeling of extreme rainfall data.

Highlighted impact of risk choice on dependence structure.

Abstract

Max-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen variables. $r$-Pareto processes are mathematically simpler and have the potential advantage of incorporating all relevant extreme events, by generalizing the notion of a univariate exceedance. In this paper we investigate score matching for performing high-dimensional peaks over threshold inference, focusing on extreme value processes associated to log-Gaussian random functions and discuss the behaviour of the proposed estimators for regularly-varying distributions with normalized marginals. Their performance is assessed on grids with several hundred locations, simulating from both the true model and from its domain of attraction. We illustrate the potential and flexibility of our methods by modelling extreme rainfall on a grid with $3600$ locations, based on risks for exceedances over local quantiles and for large spatially accumulated rainfall, and briefly discuss diagnostics of model fit. The differences between the two fitted models highlight the importance of the choice of risk and its impact on the dependence structure.