Document de travail

Extremile Regression

Abdelaati Daouia, Irene Gijbels et Gilles Stupfler

Résumé

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 spec- tral 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 func- tion 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.

Mots-clés

Asymmetric least squares; Extremes; Heavy tails; Regression extremiles; Regression quantiles; Tail index.;

Remplacé par

Abdelaati Daouia, Irene Gijbels et Gilles Stupfler, « Extremile Regression », Journal of the American Statistical Association, janvier 2021.

Référence

Abdelaati Daouia, Irene Gijbels et Gilles Stupfler, « Extremile Regression », TSE Working Paper, n° 21-1176, janvier 2021.

Voir aussi

Publié dans

TSE Working Paper, n° 21-1176, janvier 2021