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Multivariate peaks-over-threshold with latent variable representations of generalized Pareto vectors

Authors :
Bacro, Jean-Noel
Gaetan, Carlo
Opitz, Thomas
Toulemonde, Gwladys
Institut Montpelliérain Alexander Grothendieck (IMAG)
Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)
University of Ca’ Foscari [Venice, Italy]
Biostatistique et Processus Spatiaux (BioSP)
Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)
Littoral, Environment: MOdels and Numerics (LEMON)
Inria Sophia Antipolis - Méditerranée (CRISAM)
Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Montpelliérain Alexander Grothendieck (IMAG)
Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Hydrosciences Montpellier (HSM)
Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)
programme LEFE/INSU
Publication Year :
2023
Publisher :
HAL CCSD, 2023.

Abstract

Generalized Pareto distributions with positive tail index arise from embedding a Gamma random variable for the rate of an exponential distribution. In this paper, we exploit this property to define a flexible and statistically tractable modeling framework for multivariate extremes based on componentwise ratios between any two random vectors with exponential and Gamma marginal distributions. To model multivariate threshold exceedances, we propose hierarchical constructions using a latent random vector with Gamma margins, whose Laplace transform is key to obtaining the multivariate distribution function. The extremal dependence properties of such constructions, covering asymptotic independence and asymptotic dependence, are studied. We detail two useful parametric model classes: the latent Gamma vectors are sums of independent Gamma components in the first construction (called the convolution model), whereas they correspond to chi-squared random vectors in the second construction. Both of these constructions exhibit asymptotic independence, and we further propose a parametric extension (called beta-scaling) to obtain asymptotic dependence. We demonstrate good performance of likelihood-based estimation of extremal dependence summaries for several scenarios through a simulation study for bivariate and trivariate Gamma convolution models, including a hybrid model mixing bivariate subvectors with asymptotic dependence and independence.

Details

Language :
English
Database :
OpenAIRE
Accession number :
edsair.dedup.wf.001..2059bec42519b16b36ae854e3d823936