Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions

Aboubacrène Ag Ahmad; El Hadji Deme; Aliou Diop; Stéphane Girard

doi:10.1515/demo-2019-0021

Journal articles

Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions

Aboubacrène Ag Ahmad ^{1, 2} El Hadji Deme ^{1, 2} Aliou Diop ^{1, 2} Stéphane Girard ^{3, 2}

1 LERSTAD - laboratoire d'Etudes et de recherches en Statistiques et Développement

2 LIRIMA - Laboratoire International de Recherche en Informatique et Mathématiques Appliquées

3 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems

Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology

Abstract : We introduce a location-scale model for conditional heavy-tailed distributions when the covariate is deterministic. First, nonparametric estimators of the location and scale functions are introduced. Second, an estimator of the conditional extreme-value index is derived. The asymptotic properties of the estimators are established under mild assumptions and their finite sample properties are illustrated both on simulated and real data.

Keywords : conditional quantile extreme- values location-scale function extreme-values tail-index Nonparametric estimation

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Journal articles

Domain :

Mathematics [math] / Statistics [math.ST]

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https://hal.inria.fr/hal-02132976
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Submitted on : Friday, November 15, 2019 - 10:34:02 AM
Last modification on : Friday, July 3, 2020 - 4:49:10 PM

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