Computational Validation of an Adaptative Choice of Optimal Sample Fractions

For heavy-tailed models and through the use of probability weighted moments based on the largest observations (Xn-k:n ≤ ... ≤ Xn-1:n ≤ Xn:n), where Xi:n denotes the i-th ascending order statistic, we deal with the semi-parametric estimation of the extreme value index, the primary parameter in statistics of extremes. Due to the specifity of the estimators, we propose the use of bootstrap computer intensive methods for an adaptive choice of the optimal k, the number of order statistics to be used in the estimation. The developed methodology is applied to real data sets.