Multivariate peaks-over-threshold with latent variable representations of generalized Pareto vectors - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

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

Résumé

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.
Fichier principal
Vignette du fichier
Multivariate_POT_BGOT.pdf (450.22 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03965533 , version 1 (31-01-2023)

Identifiants

  • HAL Id : hal-03965533 , version 1

Citer

Jean-Noel Bacro, Carlo Gaetan, Thomas Opitz, Gwladys Toulemonde. Multivariate peaks-over-threshold with latent variable representations of generalized Pareto vectors. 2023. ⟨hal-03965533⟩
88 Consultations
118 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More