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Flexible Modeling of Non-Stationary Extremal Dependence Using Spatially-Fused LASSO and Ridge Penalties

Statistical modeling of a nonstationary spatial extremal dependence structure is a challenging problem. In practice, parametric max-stable processes are commonly used for modeling spatially-indexed block maxima data, where the stationarity assumption is often made to make inference easier. However, this assumption is unreliable for data observed over a large or complex domain. In this work, we develop a computationally-efficient method to estimate nonstationary extremal dependence using max-stable processes, which builds upon and extends an approach recently proposed in the classical geostatistical literature. More precisely, we divide the spatial domain into a fine grid of subregions, each having its own set of dependence-related parameters, and then impose LASSO ($L_1$) or Ridge ($L_2$) penalties to obtain spatially-smooth estimates. We then also subsequently merge the subregions sequentially together with a new algorithm to enhance the model's performance. Here we focus on the popular Brown-Resnick process, although extensions to other classes of max-stable processes are also possible. We discuss practical strategies for adequately defining the subregions and merging them back together. To make our method suitable for high-dimensional datasets, we exploit a pairwise likelihood approach and discuss the choice of pairs to achieve reasonable computational and statistical efficiency. We apply our proposed method to a dataset of annual maximum temperature in Nepal and show that our approach fits reasonably and realistically captures the complex non-stationarity in the extremal dependence.

Identiferoai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/676508
Date05 April 2022
CreatorsShao, Xuanjie
ContributorsHuser, Raphaƫl, Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division, Sun, Ying, Gomes, Diogo A.
Source SetsKing Abdullah University of Science and Technology
LanguageEnglish
Detected LanguageEnglish
TypeThesis

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