A Simulation Study on the Performance of Extreme-Value Index Estimators and Proposed Robustifying Modifications

The key issue of extreme-value theory is the estimation of a parameter γ, known as extreme value index. In this paper we review several extreme-value index estimators, ranging from the oldest ones to the most recent developments. Moreover, a smoothing procedure of these estimators are presented. A simulation study is conducted in order to compare the behaviour of the estimators and their smoothed alternatives. Maybe the most prominent results of this study is that no uniformly best estimator exists and that the behaviour of estimators depends on the value of the parameter γ itself.