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Caeiro, F., & Gomes D. S. R. P. (2015).  Adaptive estimation of a tail shape second order parameter. International Conference of Computational Methods in Sciences and Engineering 2015 (ICCMSE 2015). , 2015/12/31: American Institute of Physics Inc. Abstract

In Statistics of Extremes, the tail shape second order parameter is a relevant parameter whenever we want to improve the estimation of first order parameters. We shall consider two semi-parametric estimators of the shape second order parameter, parameterized with a tuning parameter. We provide a Monte Carlo comparative simulation study of several algorithms for the choice of such tuning parameter and for an adaptive estimation of the shape second order parameter.In Statistics of Extremes, the tail shape second order parameter is a relevant parameter whenever we want to improve the estimation of first order parameters. We shall consider two semi-parametric estimators of the shape second order parameter, parameterized with a tuning parameter. We provide a Monte Carlo comparative simulation study of several algorithms for the choice of such tuning parameter and for an adaptive estimation of the shape second order parameter.

Lita da Silva, J., Caeiro F., Natário I., & Braumann C. A. (2013).  Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. , Berlin Heidelberg: Springerproductflyer_978-3-642-34903-4.pdf
Caeiro, F., Gomes M. I., & Pestana D. (2009).  Alguns resultados adicionais sobre a variância de um estimador de viés reduzido do índice de cauda.. (Oliveira, I., Correia, E., Ferreira, F. Dias, S. e Braumann, C., Ed.).Actas do XVI Congresso Anual da Sociedade Portuguesa de Estatística - "Arte de Explicar o Acaso".. Abstract2009spe_art016.pdf

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F., C., Gomes, & M.I. (2013).  Asymptotic Comparison at Optimal Levels of Minimum-Variance Reduced-Bias Tail-Index Estimators. Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. 83-91., Jan: Springer Berlin Heidelberg Abstract
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Caeiro, F., & Gomes M. I. (2010).  An asymptotically unbiased moment estimator of a negative extreme value index.. Discuss. Math., Probab. Stat.. 30, 5-19., Number 1 Abstract

{Summary: We consider a new class of consistent semi-parametric estimators of a negative extreme value index, based on the set of the $k$ largest observations. This class of estimators depends on a control or tuning parameter, which enables us to have access to an estimator with a null second-order component of asymptotic bias, and with a rather interesting mean squared error, as a function of $k$. We study the consistency and asymptotic normality of the proposed estimators. Their finite sample behaviour is obtained through Monte Carlo simulation.}