Title: On a minimum distance procedure to select the optimal sample fraction in extreme value estimation
Authors: Holger Drees - University of Hamburg (Germany) [presenting]
Anja Janssen - KTH Royal Institue of Technology (Sweden)
Sid Resnick - Cornell University (United States)
Tiandong Wang - Cornell University (United States)
Abstract: Many estimators of the extreme value index and other tail parameters use a certain fraction of largest observations. The data-driven choice of this fraction is a notoriously difficult problem. A previous influential paper suggested fitting a generalized Pareto distribution (GPD) to the top $k$ order statistics for all possible $k$ and choose the value that minimizes the Kolmogorov-Smirnov distance between the fitted GPD and the empirical cdf of the exceedances. By the example of the Hill estimator, we will argue why this minimum distance approach usually leads to an inefficient tail estimator. In particular, a serious underestimation of the optimal sample fraction leads to a largely increased asymptotic variance, which can also be observed in simulations.