Title: Extreme expectile estimation in heavy-tailed regression models
Authors: Yasser Abbas - Fondation Jean-Jacques Laffont (France) [presenting]
Abdelaati Daouia - Toulouse School of Economics (France)
Gilles Stupfler - ENSAI and CREST (France)
Abstract: Studying rare events at the heavy tails of Pareto-type distributions is a burgeoning science and has many applications both in and out of finance. Most attempts to tackle the subject involve quantile regression, which usually offers a natural way of examining the impact of covariates at different levels of the dependent variable. We argue, however, that quantiles are not well equipped to deal with sparsity around the tails, especially in the active field of risk management where they fail to satisfy the coherency axiom, and motivate their least-square analogues, expectiles, as a more appropriate alternative. We introduce versatile estimators of extreme conditional expectiles under an additive regression model with heavy-tailed noise and derive their asymptotic properties in a general setting. We then tailor the discussion to the linear and local linear estimation settings. We showcase the performance of our procedures in a detailed simulation study and apply them to a concrete dataset.