@article{Oliveira_Gomes_Fraga Alves_2006, title={Improvements in the Estimation of a Heavy Tail}, volume={4}, url={https://revstat.ine.pt/index.php/REVSTAT/article/view/29}, DOI={10.57805/revstat.v4i2.29}, abstractNote={<p>In this paper, and in a context of regularly varying tails, we suggest new tail index estimators, which provide interesting alternatives to the classical Hill estimator of the tail index <em>γ</em>. They incorporate some extra knowledge on the pattern of scaled top order statistics and seem to work generally pretty well in a semi-parametric context, even for cases where a second order condition does not hold or we are outside Hall’s class of models. We shall give particular emphasis to a class of statistics dependent on a tuning parameter τ , which is merely a change in the scale of our data, from <em>X</em> to <em>X/τ</em> . Such a statistic is non-invariant both for changes in location and in scale, but compares favourably with the Hill estimator for a class of models where it is not easy to find competitors to this classic tail index estimator. We thus advance with a slight “controversial” argument: it is always possible to take advantage from a non-invariant estimator, playing with particular tuning parameters — either a change in the location or in the scale of our data —, improving then the overall performance of the classical estimators of extreme events parameters.</p>}, number={2}, journal={REVSTAT-Statistical Journal}, author={Oliveira , Orlando and Gomes , M. Ivette and Fraga Alves , M. Isabel}, year={2006}, month={Jun.}, pages={81–109} }