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Name: Gilles Stupfler

Talk Title: Extremile regression

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. We provide the first detailed study exploring the estimation of regression extremiles in the presence of covariates. In particular we extend extremile regression far into the tails of heavy-tailed distributions. Extrapolated estimators are constructed and their asymptotic theory is developed. Real data applications will be discussed to conclude the talk.

This talk is a contributed talk at EVA 2021.