Related papers: Spatial extremes: Models for the stationary case

The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition…

Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter…

Natural disasters may have considerable impact on society as well as on (re)insurance industry. Max-stable processes are ideally suited for the modeling of the spatial extent of such extreme events, but it is often assumed that there is no…

In recent years, parametric models for max-stable processes have become a popular choice for modeling spatial extremes because they arise as the asymptotic limit of rescaled maxima of independent and identically distributed random…

Environmental data science for spatial extremes has traditionally relied heavily on max-stable processes. Even though the popularity of these models has perhaps peaked with statisticians, they are still perceived and considered as the…

A central issue in the theory of extreme values focuses on suitable conditions such that the well-known results for the limiting distributions of the maximum of i.i.d. sequences can be applied to stationary ones. In this context, the…

Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models…

For many environmental processes, recent studies have shown that the dependence strength is decreasing when quantile levels increase. This implies that the popular max-stable models are inadequate to capture the rate of joint tail decay,…

Statistical methods for inference on spatial extremes of large datasets are yet to be developed. Motivated by standard dimension reduction techniques used in spatial statistics, we propose an approach based on empirical basis functions to…

Extreme environmental events such as severe storms, drought, heat waves, flash floods, and abrupt species collapse have become more prevalent in the earth-atmosphere dynamic system in recent years. In order to fully understand the…

The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…

Modeling nonstationarity that often prevails in extremal dependence of spatial data can be challenging, and typically requires bespoke or complex spatial models that are difficult to estimate. Inference for stationary and isotropic models…

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…

We tackle the modeling of threshold exceedances in asymptotically independent stochastic processes by constructions based on Laplace random fields. These are defined as Gaussian random fields scaled with a stochastic variable following an…

We consider stationary configurations of points in Euclidean space which are marked by positive random variables called scores. The scores are allowed to depend on the relative positions of other points and outside sources of randomness.…

In this paper, we introduce a new class of models for spatial data obtained from max-convolution processes based on indicator kernels with random shape. We show that this class of models have appealing dependence properties including tail…

We investigate a family of discrete-time stationary processes defined by multiple stable integrals and renewal processes with infinite means. The model may exhibit behaviors of short-range or long-range dependence, respectively, depending…

Classical models for multivariate or spatial extremes are mainly based upon the asymptotically justified max-stable or generalized Pareto processes. These models are suitable when asymptotic dependence is present, i.e., the joint tail…

The modeling of spatio-temporal trends in temperature extremes can help better understand the structure and frequency of heatwaves in a changing climate. Here, we study annual temperature maxima over Southern Europe using a century-spanning…

The goal of this paper is two-fold: 1. We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. 2. We discuss recent concepts of heavy-tailed time series,…