A class of weighted Hill estimators. Issue 6 (3rd May 2021) - Caeiro, Frederico; Mateus, Ayana; Soltane, Louiza
Abstract: In Statistics of Extremes, the estimation of the extreme value index is an essential requirement for further tail inference. In this work, we deal with the estimation of a strictly positive extreme value index from a model with a Pareto‐type right tail. Under this framework, we propose a new class of weighted Hill estimators, parameterized with a tuning parameter a . We derive their non‐degenerate asymptotic behavior and analyze the influence of the tuning parameter in such result. Their finite sample performance is analyzed through a Monte Carlo simulation study. A comparison with other important extreme value index estimators from the literature is also provided.