Extremile regression

Abdelaati Daouia, Irene Gijbels and Gilles Stupfler
Additional contact information
Abdelaati Daouia: 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

Post-Print from HAL

Abstract: Regression extremiles define a least squares analogue of regression quantiles. They are determined by weighted expectations rather than tail probabilities. Of special interest is their intuitive meaning in terms of expected minima and maxima. Their use appears naturally in risk management where, in contrast to quantiles, they fulfill the coherency axiom and take the severity of tail losses into account. In addition, they are comonotonically additive and belong to both the families of spectral risk measures and concave distortion risk measures. This paper provides the first detailed study exploring implications of the extremile terminology in a general setting of presence of covariates. We rely on local linear (least squares) check function minimization for estimating conditional extremiles and deriving the asymptotic normality of their estimators. We also extend extremile regression far into the tails of heavy-tailed distributions. Extrapolated estimators are constructed and their asymptotic theory is developed. Some applications to real data are provided.

Keywords: Asymmetric least squares; Extremes; Heavy tails; Regression extremiles; Regression quantiles; Tail index. (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Published in Journal of the American Statistical Association, inPress, 116, ⟨10.1080/01621459.2021.1875837⟩

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
Working Paper: Extremile Regression (2024)
Working Paper: Extremile Regression (2024)
Journal Article: Extremile Regression (2022)
Working Paper: Extremile Regression (2021)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03181017

DOI: 10.1080/01621459.2021.1875837

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().