A1347
Title: Extreme value theory-based kernel smoothing for tail probability estimation
Authors: Taku Moriyama - Yokohama City University (Japan) [presenting]
Abstract: For estimating tail probabilities, several methods have been proposed, including approximations for threshold exceedances based on extreme value theory and HallWeissman-type approaches. However, motivated by concerns about the accuracy of the extreme-value approximations underlying these estimators, a new balloon-type kernel smoothing estimator is proposed. Kernel smoothing estimators involve a smoothing parameter, or bandwidth, which plays the role of regularization. In the present setting, however, the bandwidth should be chosen to minimize the local error in the tail region, rather than the conventional global error. This naturally leads to a point-dependent, balloon-type bandwidth. Standard kernel smoothing estimators are shown not to be well suited to tail probability estimation. Nevertheless, by carefully modifying the construction of the estimator, tail probabilities can be estimated effectively. The proposed estimator is shown not to require, in general, approximations based on extreme value theory.
