TY  - RPRT
CY  - Toulouse
ID  - publications42257
UR  - https://www.tse-fr.eu/sites/default/files/TSE/documents/doc/wp/2021/wp_tse_1176.pdf
A1  - Daouia, Abdelaati
A1  - Gijbels, Irene
A1  - Stupfler, Gilles
Y1  - 2021/01//
N2  - 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.
PB  - TSE Working Paper
T3  - TSE Working Paper
KW  - Asymmetric least squares
KW  - Extremes
KW  - Heavy tails
KW  - Regression extremiles
KW  - Regression quantiles
KW  - Tail index.
M1  - working_paper
TI  - Extremile Regression
AV  - public
EP  - 33
ER  -