Modeling Spatial Processes with Unknown Extremal Dependence Class

By Raphaël Huser, Jennifer L. Wadsworth. Journal of the American Statistical Association, 2017

149 citations recorded by the source corpus.

ABSTRACT Many environmental processes exhibit weakening spatial dependence as events become more extreme. Well-known limiting models, such as max-stable or generalized Pareto processes, cannot capture this, which can lead to a preference for models that exhibit a property known as asymptotic independence. However, weakening dependence does not automatically imply asymptotic independence, and whether the process is truly asymptotically (in)dependent is usually far from clear. The distinction is key as it can have a large impact upon extrapolation, that is, the estimated probabilities of events more extreme than those observed. In this work, we present a single spatial model that is able to capture both dependence classes in a parsimonious manner, and with a smooth transition between the two cases. The model covers a wide range of possibilities from asymptotic independence through to complete dependence, and permits weakening dependence of extremes even under asymptotic dependence. Censored likelihood-based inference for the implied copula is feasible in moderate dimensions due to closed-form margins. The model is applied to oceanographic datasets with ambiguous true limiting dependence structure. Supplementary materials for this article are available online.

Subfields: Environmental Engineering, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1716917a2f414cf8d42d6adb1e3eee4344f28e48

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Citations in the corpus

INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles (2018, background): “…framework to more complex spatial (Wadsworth and Tawn, 2012; Thibaud et al. , 2013; Thibaud and Opitz, 2015; Huser et al. , 2017; Castro Camilo and Huser, 2017; Huser and Wadsworth, 2018) and spatio-temporal (Davis et al. , 2013; Huser and Davison, 2014; Bacro et al. , 2017) models for extremes.”
Functional peaks‐over‐threshold analysis (2020, background): “Huser et al. (2017) and Huser and Wadsworth (2019) have proposed spatial models in which dependence decreases that could be extended to our setting.”
A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach (2018, methodology): “Recent development on Generalized Pareto Processes allow for considering parametric estimation for the dependence structure, see, e.g. Ferreira and De Haan (2014), Thibaud and Opitz (2015) and Huser and Wadsworth (2017).”