A class of weighted Hill estimators

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.

Box-Cox Transformations and Bias Reduction in Extreme Value Theory

“…The estimator in Equation (15) will be used in Section 4 for comparison with the new class of MVRB EVI estimators introduced in this paper. Other techniques have been used in the literature to reduce the bias of the Hill estimator, in Equation ( 14), and new estimators based on generalized means or norms that generalize the Hill estimator have been proposed (see Brilhante et al [25], Caeiro et al [26][27][28][29], Paulauskas and Vaiciulis [8,9], Beran et al [30], and Beirlant et al [31], among others).…”