Title: Extreme expectile regression in heavy-tailed regression models
Authors: Yasser Abbas - Fondation Jean-Jacques Laffont (France) [presenting]
Abstract: Studying rare events at the tails of heavy-tailed 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, and motivate their least-square analogues, expectiles, as a more appropriate alternative. We introduce versatile estimators of tail conditional expectiles under an extremal additive regression model with heavy-tailed regression noise and derive their asymptotic properties in a general setting. We then tailor the discussion to the local linear estimation approach. We showcase the performance of our procedures in a detailed simulation study and apply them to a concrete dataset.