Reduced bias and threshold choice in the extremal index estimation through resampling techniques

InExtreme ValueAnalysisthere are a few parameters of particular interest among which we refer to theextremal index, a measure ofextreme eventsclustering.It is of great interest for initial dependent samples, the common situation in many practical situations. Most semi-parametric estimators of this parameter show the same behavior: nice asymptoticpropertiesbut a high variance for small values ofk, the number of upper order statistics used in the estimation and a high bias for large values ofk. The Mean Square Error, a measure that encompasses bias and variance, usually shows a very sharp plot, needing an adequate choice ofk. Using classicalextremal indexestimators considered in the literature, the emphasis is now given to derive reduced bias estimators with more stable paths, obtained through resampling techniques. An adaptive algorithm for estimating the levelkfor obtaining a reliable estimate of theextremal indexis used. This algorithm has shown good results, but some improvements are still required. A simulation study will illustrate thepropertiesof the estimators and the performance of the adaptive algorithm proposed.