Resampling-Based Methodologies in Statistics of Extremes: Environmental and Financial Applications

Resampling computer intensive methodologies, like the jackknife and the bootstrap are important tools for a reliable semi-parametric estimation of parameters of extreme or even rare events. Among these parameters we mention the extreme value index, ξ, the primary parameter in statistics of extremes. Most of the semi-parametric estimators of this parameter show the same type of behaviour: nice asymptotic properties, but a high variance for small k, the number of upper order statistics used in the estimation, a high bias for large k, and the need for an adequate choice of k. After a brief reference to some estimators of the aforementioned parameter and their asymptotic properties we present an algorithm that deals with an adaptive reliable estimation of ξ. Applications of these methodologies to the analysis of environmental and financial data sets are undertaken.

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