Efficient inference and simulation for elliptical Pareto processes

By Emeric Thibaud, Thomas Opitz. 2013

108 citations recorded by the source corpus.

Recent advances in extreme value theory have established $\ell$-Pareto processes as the natural limits for extreme events defined in terms of exceedances of a risk functional. Here we provide methods for the practical modelling of data based on a tractable yet flexible dependence model. We introduce the class of elliptical $\ell$-Pareto processes, which arise as the limit of threshold exceedances of certain elliptical processes characterized by a correlation function and a shape parameter. An efficient inference method based on maximizing a full likelihood with partial censoring is developed. Novel procedures for exact conditional and unconditional simulation are proposed. These ideas are illustrated using precipitation extremes in Switzerland.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7e28d2cbf57b49749beea9f6a021d96819acc755

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Citations in the corpus

Non-Stationary Dependence Structures for Spatial Extremes (2014, methodology): “, 2013; Huser and Davison, 2014), although more efficient approaches based on the point process characterization of extremes have recently been proposed (Wadsworth and Tawn, 2014; Thibaud and Opitz, 2014; Engelke et al., 2014).”
Likelihood estimators for multivariate extremes (2014, background): “…(26) and (27) require that all the mass of the exponent measure is distributed on the interior of its domain of definition (as for the logistic model), and are unsuitable if some positive mass lies on the boundary faces or edges (as for the asymmetric logistic model); see Thibaud and Opitz (2015).”
INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles (2018, background): “…threshold-based approaches to environmental extremes observed over space and/or time have since been published; see, e.g., Huser and Davison (2014), Thibaud and Opitz (2015) and Bacro et al. (2017) for recent applications to precipitation data, Chavez-Demoulin and Davison (2005) for temperature…”
Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures (2016, methodology): “…exceedances based on the limiting Poisson (Wadsworth and Tawn, 2014; Engelke et al., 2015) or the generalized Pareto (Ferreira and de Haan, 2014; Thibaud and Opitz, 2015) process are the counter-parts of max-stable models for threshold exceedances and have become increasingly popular because…”
A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach (2018, methodology): “Recent development on Generalized Pareto Processes allow for considering parametric estimation for the dependence structure, see, e.g. Ferreira and De Haan (2014), Thibaud and Opitz (2015) and Huser and Wadsworth (2017).”
Decompositions of dependence for high-dimensional extremes (2016, methodology): “The same data were analyzed by Thibaud and Opitz (2015) and were found to be asymptotically dependent.”
Extremes on river networks (2015, unknown): “Recent research has focused on methods that exploit full likelihoods of multivariate extreme observations through peaks-over-threshold approaches (Wadsworth and Tawn, 2014; Engelke et al., 2015; Thibaud and Opitz, 2014; Bienvenüe and Robert, 2014), and on M -estimators for spatial extremes (Einmahl ”
Functional peaks‐over‐threshold analysis (2020, background): “Thibaud and Opitz (2015), for instance, suppose that the corresponding random variable Nu is fixed and use a binomial distribution, which is easily linked to the Poisson point process model.”