@article{Penalva_Gomes_Caeiro_Neves_2020, title={A Couple of Non Reduced Bias Generalized Means in Extreme Value Theory: An Asymptotic Comparison}, volume={18}, url={https://revstat.ine.pt/index.php/REVSTAT/article/view/301}, DOI={10.57805/revstat.v18i3.301}, abstractNote={<p>Lehmer’s mean-of-order <em>p</em> (L<sub>p</sub>) generalizes the arithmetic mean, and L<sub>p</sub> extreme value index (EVI)-estimators can be easily built, as a generalization of the classical Hill EVI-estimators. Apart from a reference to the asymptotic behaviour of this class of estimators, an asymptotic comparison, at optimal levels, of the members of such a class reveals that for the optimal (<em>p, k</em>) in the sense of minimal mean square error, with <em>k</em> the number of top order statistics involved in the estimation, they are able to overall outperform a recent and promising generalization of the Hill EVI-estimator, related to the power mean, also known as H¨older’s mean-of-order-<em>p</em>. A further comparison with other ‘classical’ non-reduced-bias estimators still reveals the competitiveness of this class of EVI-estimators.</p>}, number={3}, journal={REVSTAT-Statistical Journal}, author={Penalva , Helena and Gomes , M. Ivette and Caeiro , Frederico and Neves , M. Manuela}, year={2020}, month={Aug.}, pages={281–298} }