Bridging Asymptotic Independence and Dependence in Spatial Extremes Using Gaussian Scale Mixtures

TL;DR

This paper introduces flexible Gaussian scale mixture models that unify asymptotic dependence and independence in spatial extremes, enabling better modeling of tail behavior in environmental data.

Contribution

It develops new parametric copula models that interpolate between dependence types and demonstrates their effectiveness on wind speed data.

Findings

Models accurately capture extremal dependence in wind speed data.

Parametric models outperform nonparametric statistics in estimating tail dependence.

Method provides a unified framework for spatial extreme modeling.

Abstract

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study in detail the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose several flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. Our parametric approach outperforms the widely used nonparametric $\chi$ and $\bar\chi$ statistics often used to guide model choice at an exploratory stage by borrowing strength across locations for better estimation of the asymptotic dependence class. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.