Extreme Conditional Expectile Estimation in Heavy-Tailed Heteroscedastic Regression Models - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Annals of Statistics Year : 2021

Extreme Conditional Expectile Estimation in Heavy-Tailed Heteroscedastic Regression Models

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.
Fichier principal
Vignette du fichier
fullpaper.pdf (3.89 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03306230 , version 1 (03-04-2020)
hal-03306230 , version 2 (03-12-2020)
hal-03306230 , version 3 (22-04-2021)
hal-03306230 , version 4 (17-08-2021)
hal-03306230 , version 5 (07-04-2022)
hal-03306230 , version 6 (13-04-2022)
hal-03306230 , version 7 (16-01-2024)

Identifiers

Cite

Stéphane Girard, Gilles Claude Stupfler, Antoine Usseglio-Carleve. Extreme Conditional Expectile Estimation in Heavy-Tailed Heteroscedastic Regression Models. Annals of Statistics, 2021, 49 (6), pp.3358--3382. ⟨10.1214/21-AOS2087⟩. ⟨hal-03306230v7⟩
1252 View
930 Download

Altmetric

Share

Gmail Facebook X LinkedIn More