Extremal t processes: Elliptical domain of attraction and a spectral representation

Abstract

The extremal t process was proposed in the literature for modeling spatial extremes within a copula framework based on the extreme value limit of elliptical t distributions (Davison, Padoan and Ribatet (2012)). A major drawback of this max-stable model was the lack of a spectral representation such that for instance direct simulation was infeasible. The main contribution of this note is to propose such a spectral construction for the extremal t process. Interestingly, the extremal Gaussian process introduced by Schlather (2002) appears as a special case. We further highlight the role of the extremal t process as the maximum attractor for processes with finite-dimensional elliptical distributions. All results naturally also hold within the multivariate domain.

References in corpus (6)

• Statistical Modeling of Spatial Extremes
• Stationary max-stable fields associated to negative definite functions
• Max-stable models for multivariate extremes
• Conditional simulations of Brown-Resnick processes
• Regular conditional distributions of max infinitely divisible processes
• Conditional simulation of extremal Gaussian processes

Cited by in corpus (19)

• Space-time modelling of extreme events
• Extremes on river networks
• Efficient inference and simulation for elliptical Pareto processes
• Bayesian inference for the Brown-Resnick process, with an application to extreme low temperatures
• Modeling asymptotically independent spatial extremes based on Laplace random fields
• Extremal attractors of Liouville copulas
• A two-step approach to model precipitation extremes in California based on max-stable and marginal point processes
• Optimal Bayesian design for model discrimination via classification
• ABC model selection for spatial extremes models applied to South Australian maximum temperature data
• Hierarchical space-time modeling of exceedances with an application to rainfall data
• Non-stationary max-stable models with an application to heavy rainfall data
• Non-Stationary Dependence Structures for Spatial Extremes
• High-order Composite Likelihood Inference for Max-Stable Distributions and Processes
• Censored pairwise likelihood-based tests for mixing coefficient of spatial max-mixture models
• High-dimensional inference using the extremal skew-$t$ process
• Generalised least squares estimation of regularly varying space-time processes based on flexible observation schemes
• A Dimension-Reduced Multivariate Spatial Model for Extreme Events: Balancing Flexibility and Scalability
• A Bayesian semi-parametric hybrid model for spatial extremes with unknown dependence structure
• Bridging Asymptotic Independence and Dependence in Spatial Extremes Using Gaussian Scale Mixtures