Extreme Conditional Expectile Estimation in Heavy-Tailed Heteroscedastic Regression Models

Stéphane Girard (), Gilles Stupfler and Antoine Usseglio-Carleve
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Stéphane Girard: STATIFY - Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension - Centre Inria de l'Université Grenoble Alpes - Inria - Institut National de Recherche en Informatique et en Automatique - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes
Antoine Usseglio-Carleve: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: Expectiles define a least squares analogue of quantiles. They have been the focus of a substantial quantity of research in the context of actuarial and financial risk assessment over the last decade. The behaviour and estimation of unconditional extreme expectiles using independent and identically distributed heavy-tailed observations has been investigated in a recent series of papers. We build here a general theory for the estimation of extreme conditional expectiles in heteroscedastic regression models with heavy-tailed noise; our approach is supported by general results of independent interest on,residual-based extreme value estimators in heavy-tailed regression models, and is intended to cope with covariates having a large but fixed dimension. We demonstrate how our results can be applied to a wide class of important examples, among which linear models, single-index models as well as ARMA and GARCH time series models. Our estimators are showcased on a numerical simulation study and on real sets of actuarial and financial data.

Keywords: Expectiles; Extreme value analysis; Heavy-tailed distribution; Heteroscedasticity; Regression models; Single-indes model; Residual-based estimators; Tail empirical process of residuals (search for similar items in EconPapers)
Date: 2021-12
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-isf
Note: View the original document on HAL open archive server: https://hal.science/hal-03306230v7
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Citations: View citations in EconPapers (16)

Published in Annals of Statistics, 2021, 49 (6), pp.3358--3382. ⟨10.1214/21-AOS2087⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03306230

DOI: 10.1214/21-AOS2087

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