Modeling asymptotically independent spatial extremes based on Laplace random fields

TL;DR

This paper introduces a novel framework for modeling asymptotically independent spatial extremes using Laplace random fields, which better capture joint tail behavior and improve fit for extreme wind gust data.

Contribution

It develops a Laplace random field-based approach for asymptotic independence modeling, with theoretical properties and practical inference demonstrated on wind gust data.

Findings

Laplace fields exhibit slower joint tail decay than Gaussian fields with same covariance.

The method provides more conservative estimates of joint extreme risks.

Application shows better fit to wind gust extremes compared to Gaussian models.

Abstract

We tackle the modeling of threshold exceedances in asymptotically independent stochastic processes by constructions based on Laplace random fields. These are defined as Gaussian random fields scaled with a stochastic variable following an exponential distribution. This framework yields useful asymptotic properties while remaining statistically convenient. Univariate distribution tails are of the half exponential type and are part of the limiting generalized Pareto distributions for threshold exceedances. After normalizing marginal tail distributions in data, a standard Laplace field can be used to capture spatial dependence among extremes. Asymptotic properties of Laplace fields are explored and compared to the classical framework of asymptotic dependence. Multivariate joint tail decay rates for Laplace fields are slower than for Gaussian fields with the same covariance structure; hence they provide more conservative estimates of very extreme joint risks while maintaining asymptotic independence. Statistical inference is illustrated on extreme wind gusts in the Netherlands where a comparison to the Gaussian dependence model shows a better goodness-of-fit in terms of Akaike's criterion. In this specific application we fit the well-adapted Weibull distribution as univariate tail model, such that the normalization of univariate tail distributions can be done through a simple power transformation of data.