Computer intensive methods for improving the extremal index estimation

Resampling methodologies have revealed recently as important tools in semi-parametric estimation of parameters in the field of extremes. Among a few parameters of interest, we are here interested in the extremal index, a measure of the degree of local dependence in the extremes of a stationary sequence. Most semi-parametric estimators of this parameter show the same type of behavior: nice asymptotic properties but a high variance for small values of k, the number of upper order statistics used in the estimation and a high bias for large values of k. Two extremal index estimators are here considered: a classical one and a reduced-bias generalized jackknife estimator. Bootstrap and jackknife methodologies are applied for obtaining the "best block size" for resampling and then constructing the bootstrap version of those estimators, that have led to more stable sample paths. A large simulation study was performed for illustrating the behavior of the resampling procedure proposed.