A Paper by Gilles Stupfler Published in the JASA

“Extremile Regression”, a paper by Gilles Stupfler, Lecturer in Statistics at ENSAI and researcher at CREST, Abdelaati Daouia, associate Professor at the University of Toulouse and Irène Gijbels, Professor at KU Leuven, was published in the Journal of the American Statistical Association

Journal of the American Statistical Association is a journal of statistical science that publishes research in statistical applications, theory and methods. It is widely considered as one of the top 5 statistical journals in the world. This research was carried out in the context of the ANR project ExtremReg and Gilles Stupfler’s recent award from the AXA Research Fund on “Mitigating risk in the wake of the COVID-19 pandemic”. It builds on a previous 2019 paper, also published in JASA.


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 article 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.


Asymmetric least squares / Extremes / Heavy tails / Regression extremiles / Regression quantiles / Tail index


The research of A. Daouia and G. Stupfler is supported by the French National Research Agency under the grant ANR-19-CE40-0013/ExtremReg project. A. Daouia also acknowledges funding from the ANR under grant ANR-17-EURE-0010 (Investissements d’Avenir program). I. Gijbels gratefully acknowledges support from the Research Fund KU Leuven (projects GOA/12/014 and C16/20/002), and from Research Grant FWO G0D6619N (Flemish Science Foundation). G. Stupfler also acknowledges support from an AXA Research Fund Award on “Mitigating risk in the wake of the COVID-19 pandemic.”

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Find out more about Gilles Stupfler and research at ENSAI