Non-Stationary Dependence Structures for Spatial Extremes

TL;DR

This paper develops non-stationary max-stable models for spatial extremes, allowing covariate incorporation, and demonstrates their effectiveness with temperature data over complex terrains.

Contribution

It introduces a flexible framework for modeling non-stationary spatial extremes using max-stable processes with covariates, enhancing existing stationary models.

Findings

Models accurately estimate extremal dependence

Parameters are well estimated in simulations

Effectively captures temperature maxima over complex topography

Abstract

Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable models have been developed, and fitted to various types of data. However, a recurrent problem is the modeling of non-stationarity. In this paper, we develop non-stationary max-stable dependence structures in which covariates can be easily incorporated. Inference is performed using pairwise likelihoods, and its performance is assessed by an extensive simulation study based on a non-stationary locally isotropic extremal $t$ model. Evidence that unknown parameters are well estimated is provided, and estimation of spatial return level curves is discussed. The methodology is demonstrated with temperature maxima recorded over a complex topography. Models are shown to satisfactorily capture extremal dependence.