Computational Validation of an Adaptative Choice of Optimal Sample Fractions
Frederico Caeiro1, M. Ivette Gomes2
1FCT and CMA - UNL, Portugal; 2DEIO and CEAUL - FCUL, Portugal

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.

Keywords: Heavy tails; Semi-parametric estimation; Extreme Value Index; Bootstrap Methodology

Biography: Frederico Caeiro is an Assistant Professor at Department of Mathematics, Faculty of Ciences and Tecnology - New University of Lisbon. He received an PhD in Statistics from the University of Lisbon in 2006. He is author/co-author of several articles in Extreme Value Theory.