Information Covid Research

Gilles Stupfler Publishes a Paper in the Annals of Statistics 

“Extreme conditional expectile estimation in heavy-tailed heteroscedastic regression models”, a paper co-authored by Stéphane Girard, Gilles Stupfler, Associate Professor in Statistics at ENSAI and researcher at CREST, and Antoine Usseglio-Carleve was published in Volume 49 of the Annals of Statistics.  

The Annals of Statistics is a peer-reviewed statistics journal published by the Institute of Mathematical Statistics. It is considered as the best journal in the field of mathematical statistics.

This piece of work is the culmination of two and a half years of investigations by Gilles Stupfler, Stéphane Girard and Antoine Usseglio-Carleve on the topic of extreme data analysis for the financial and insurance fields. “We started from a fairly precise requirement: to estimate conditional expectiles in order to give a less limited picture of the risk than with the quantile. We ended up putting together a broad toolkit for a substantially larger class of extreme regression problems”, explains Gilles Stupfler. The methods developed can handle heteroscedastic time-dependent data to an extent, which is crucial in finance. The paper’s parts on inference and Bootstrap were largely contributed to by Antoine Usseglio-Carleve during his postdoctoral position at ENSAI and CREST.

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 have 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 are 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, residual-based estimators, Single-index model, tail empirical process of residuals

Funding Statement

This research was supported by the French National Research Agency under the grants ANR-15-IDEX-02 and ANR-19-CE40-0013. S. Girard gratefully acknowledges the support of the Chair Stress Test, led by the French École Polytechnique and its Foundation and sponsored by BNP Paribas. G. Stupfler also acknowledges support from an AXA Research Fund Award on “Mitigating risk in the wake of the COVID-19 pandemic”. A. Usseglio-Carleve also acknowledges funding from the ANR under grant ANR-17-EURE-0010 (Investissements d’Avenir programme).

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Find out more about Gilles Stupfler and research at ENSAI.