Revisiting Resampling Methods in the Extremal Index Estimation: Improving Risk Assessment

Extreme value theory is an area of primordial importance for modelling extreme risks, allowing to estimate and predict beyond the range of data available. Among several parameters of interest, the extremal index is a crucial parameter in a dependent set-up, characterizing the degree of local dependence in the extremes of a stationary sequence. Its estimation has been addressed by several authors but some difficulties still remain. Resampling computer intensive methodologies have been recently considered in a reliable estimation of parameters of rare events. However classical bootstrap cannot be applied and block bootstrap procedures need to be considered. The block size for resampling strongly affects the estimates and needs to be properly chosen. Here, procedures for the choice of the block size for resampling are revisited and an improvement of the methods used in previous works for that choice is also considered. A simulation study will illustrate the performance of the aforementioned procedures. A real application is also presented.