Abstract
AbstractThe classical modeling of spatial extremes relies on asymptotic models (i.e., max‐stable orr‐Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often suggests that such asymptotic models are too rigidly constrained, and that they do not adequately capture the frequent situation where more severe events tend to be spatially more localized. In other words, these asymptotic models have a strong tail dependence that persists at increasingly high levels, while data usually suggest that it should weaken instead. Another well‐known limitation of classical spatial extremes models is that they are either computationally prohibitive to fit in high dimensions, or they need to be fitted using less efficient techniques. In this review paper, we describe recent progress in the modeling and inference for spatial extremes, focusing on new models that have more flexible tail structures that can bridge asymptotic dependence classes, and that are more easily amenable to likelihood‐based inference for large datasets. In particular, we discuss various types of random scale constructions, as well as the conditional spatial extremes model, which have recently been getting increasing attention within the statistics of extremes community. We illustrate some of these new spatial models on two different environmental applications.This article is categorized under:Data: Types and Structure > Image and Spatial DataData: Types and Structure > Time Series, Stochastic Processes, and Functional DataStatistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods
Highlights
KEYWORDS asymptotic dependence and independence, extreme-value theory, max-stable process, Pareto process, random scale mixture
While inverted max-stable (IMS), max-mixture, and random scale or location mixture models discussed in Sections 3.2 and 3.3 are designed to be fitted to peaks over high thresholds, we conclude this section by briefly presenting recent models designed for block maxima, which extend the class of max-stable processes to capture asymptotic independence
In contrast to Morris et al (2017) who proposed a skew-t process combined with a random partitioning mechanism to break down long-range dependence, the conditional spatial extremes model allows for very flexible forms of extremal dependence and can naturally capture both asymptotic dependence and independence
Summary
KEYWORDS asymptotic dependence and independence, extreme-value theory, max-stable process, Pareto process, random scale mixture A related limitation of max-stable and Pareto processes is that they are always asymptotically dependent, unless they are fully independent.
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