A1105
Title: Comparative study on tail probability estimation in i.i.d. settings
Authors: Taku Moriyama - Yokohama City University (Japan) [presenting]
Abstract: Tail probability estimators in i.i.d. settings are considered. There are mainly two ways for the estimation: The fitting to the generalized Pareto distribution and the fully nonparametric estimation. The fitting estimator is justified by the approximation proven in the extreme value theory; however, the accuracy depends on the target point, i.e., how extremely large the target is. The nonparametric estimator does not need the approximation and has the advantage of wide applicability; however, the optimal regularization parameter depends on both the target point and the extreme value index. Both theoretical and numerical comparative studies on tail probability estimation are conducted. Asymptotic convergence rates of estimators are obtained, and the mean integrated squared errors are numerically surveyed by a simulation study.
