Resampling procedures for a more reliable extremal index estimation

Extreme value theory (EVT) deals essentially with the estimation of parameters of extreme or rare events. One important parameter in EVT, which measures the amount of clustering in the extremes of a stationary sequence, is the extremal index. It needs to be adequately estimated, not only by itself but also due to its influence on other parameters such as a high quantile, return period or expected shortfall. This chapter discusses some classical estimators of extremal index and their asymptotic properties. It illustrates the challenges that appear for finite samples and discusses the generalized jackknife methodology that has shown to give good results in extreme value theory. The chapter provides an extensive simulation study and shows some results of the study. Finally, it applies a heuristic procedure, based on a stability criterion, to some simulated samples to estimate the extremal index.