A0796
Title: Extreme conditional quantile estimation for location-scale regression models and time series
Authors: Gilles Stupfler - University of Angers (France) [presenting]
Marco Oesting - University of Stuttgart (Germany)
Abstract: Motivated by applied questions in environmental science, finance and insurance, such as the prediction of the magnitude of a potential extreme rainfall event tomorrow given weather parameters today, or the prediction of the value of large losses on a financial asset given the overall state of a financial market, we construct conditional extreme quantile estimators in location-scale regression models based on residuals from a preliminary estimation of model structure. The crucial difficulty in order to work out the asymptotic behavior of the resulting estimators is that residuals will typically not be independent or even identically distributed, even in simple models such as linear regression. Recent work has shown that residual-based versions of extreme value estimators are consistent and asymptotically normal, just as their unachievable true error-based counterparts would be, provided the residuals are in some sense uniformly close to the corresponding regression errors. It is shown that this assumption can be substantially weakened by taking a different route, not relying on the validity of a Gaussian approximation to the so-called tail empirical process, thus leading to a theoretical framework that can, in particular, handle a large array of classical time series models without having to impose unnecessary technical restrictions.
