Practical strategies for GEV-based regression models for extremes

Castro-Camilo, D. , Huser, R. and Rue, H. (2022) Practical strategies for GEV-based regression models for extremes. Environmetrics, (doi: 10.1002/env.2742) (Early Online Publication)

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Abstract

The generalised extreme value (GEV) distribution is a three parameter family that describes the asymptotic behaviour of properly renormalised maxima of a sequence of independent and identically distributed random variables. If the shape parameter ξ is zero, the GEV distribution has unbounded support, whereas if ξ is positive, the limiting distribution is heavy-tailed with infinite upper endpoint but finite lower endpoint. In practical applications, we assume that the GEV family is a reasonable approximation for the distribution of maxima over blocks, and we fit it accordingly. This implies that GEV properties, such as finite lower endpoint in the case ξ>0, are inherited by the finite-sample maxima, which might not have bounded support. This is particularly problematic when predicting extreme observations based on multiple and interacting covariates. To tackle this usually overlooked issue, we propose a blended GEV distribution, which smoothly combines the left tail of a Gumbel distribution (GEV with ξ=0) with the right tail of a Fréchet distribution (GEV with ξ>0) and, therefore, has unbounded support. Using a Bayesian framework, we reparametrise the GEV distribution to offer a more natural interpretation of the (possibly covariate-dependent) model parameters. Independent priors over the new location and spread parameters induce a joint prior distribution for the original location and scale parameters. We introduce the concept of property-preserving penalised complexity (P3C) priors and apply it to the shape parameter to preserve first and second moments. We illustrate our methods with an application to NO2 pollution levels in California, which reveals the robustness of the bGEV distribution, as well as the suitability of the new parametrisation and the P3C prior framework.

Item Type:Articles
Additional Information:This publication is partially based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. OSR-CRG2017-3434.
Status:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Castro-Camilo, Dr Daniela
Authors: Castro-Camilo, D., Huser, R., and Rue, H.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Environmetrics
Publisher:Wiley
ISSN:1180-4009
ISSN (Online):1099-095X
Published Online:28 June 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Environmetrics 2022
Publisher Policy:Reproduced under a Creative Commons License
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