Abstract

In Extreme Value Theory (EVT) we deal essentially with the estimation of parameters of extreme or even rare events. A large number of applications in areas such as biology, environment, finance, hydrology and telecommunications, reveals the importance of adequate estimation procedures. Among the key parameters in EVT we refer to the extremal index (EI). The EI characterizes the degree of local dependence in the extremes of a stationary sequence and measures the limiting dependence of exceedances over a threshold u, as u tends to the upper endpoint of the distribution. Although some work has been done concerning the EI estimation, some difficulties still remain. After reviewing some estimators of the EI, their asymptotic properties and the difficulties they present, the goal of this work is to deal with the application of computer intensive methods together with heuristic procedures for improving the extremal index estimation. Block-bootstrap and Jackknife-After-Bootstrap are two computational procedures that have been revealing themselves as good procedures for obtaining reliable semi-parametric estimators of the EI. However the performance of resampling methods crucially depends on the block size that must be supplied by the user. That block size must be estimated and the number of upper order statistics used in the estimation needs also to be chosen. A few results of a simulation study will illustrate the application of those procedures.