Publications

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Book Chapter
Caeiro, F., & Gomes M. I.: (2014).  A semi-parametric estimator of a shape second order parameter.. (Pacheco, A.,, Santos, R.,, Rosário Oliveira, M., Paulino, C.D., Ed.).New Advances in Statistical Modeling and Applications. 137-144., Jan: Springer Abstract

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Conference Proceedings
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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Journal Article
Gomes, M. I., Caeiro F., Figueiredo F., Henriques-Rodrigues L., & Pestana D. (2020).  Corrected-Hill versus partially reduced-bias value-at-risk estimation. Communications in Statistics: Simulation and Computation. 49, 867-885., Number 4 Abstract
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Penalva, H., Ivette Gomes M., Caeiro F., & Manuela Neves M. (2020).  A couple of non reduced bias generalized means in extreme value theory: An asymptotic comparison. Revstat Statistical Journal. 18, 281-298., Number 3 Abstract
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Caeiro, F., Gomes M. I., & Pestana D. (2005).  Direct reduction of bias of the classical Hill estimator.. REVSTAT. 3, 113-136., Number 2 Abstract

{Summary: We are interested in an adequate estimation of the dominant component of the bias of ıt B. M. Hill}\,'s estimator [Ann. Stat. 3, 1163–1174 (1975; Zbl 0323.62033)] of a positive tail index $\gamma$, in order to remove it from the classical Hill estimator in different asymptotically equivalent ways. If the second order parameters in the bias are computed at an adequate level $k_1$ of a larger order than that of the level $k$ at which the Hill estimator is computed, there may be no change in the asymptotic variances of these reduced bias tail index estimators, which are kept equal to the asymptotic variance of the Hill estimator, i.e., equal to $\gamma^2$. The asymptotic distributional properties of the proposed estimators of $\gamma$ are derived and the estimators are compared not only asymptotically, but also for finite samples through Monte Carlo techniques.}

Penalva, H., Gomes M. I., Caeiro F., & Neves M. M. (2020).  Lehmer{'}s mean-of-order-p extreme value index estimation: a simulation study and applications. Journal of Applied Statistics. 47, 2825-2845., Number 13-15 Abstract
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Gomes, I. M., Brilhante F. M., Caeiro F., & Pestana D. (2015).  A new partially reduced-bias mean-of-order p class of extreme value index estimators. Computational Statistics & Data AnalysisComputational Statistics & Data Analysis. 82, 223 - 227., 2015 AbstractWebsite

A class of partially reduced-bias estimators of a positive extreme value index (EVI), related to a mean-of-order-p class of EVI-estimators, is introduced and studied both asymptotically and for finite samples through a Monte-Carlo simulation study. A comparison between this class and a representative class of minimum-variance reduced-bias (MVRB) EVI-estimators is further considered. The MVRB EVI-estimators are related to a direct removal of the dominant component of the bias of a classical estimator of a positive EVI, the Hill estimator, attaining as well minimal asymptotic variance. Heuristic choices for the tuning parameters p and k, the number of top order statistics used in the estimation, are put forward, and applied to simulated and real data.A class of partially reduced-bias estimators of a positive extreme value index (EVI), related to a mean-of-order-p class of EVI-estimators, is introduced and studied both asymptotically and for finite samples through a Monte-Carlo simulation study. A comparison between this class and a representative class of minimum-variance reduced-bias (MVRB) EVI-estimators is further considered. The MVRB EVI-estimators are related to a direct removal of the dominant component of the bias of a classical estimator of a positive EVI, the Hill estimator, attaining as well minimal asymptotic variance. Heuristic choices for the tuning parameters p and k, the number of top order statistics used in the estimation, are put forward, and applied to simulated and real data.

Gomes, M. I., Pestana D., & Caeiro F. (2009).  A note on the asymptotic variance at optimal levels of a bias-corrected Hill estimator.. Stat. Probab. Lett.. 79, 295-303., Number 3 Abstract

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Gomes, M. I., Caeiro F., Figueiredo F., Henriques-Rodrigues L., & Pestana D. (2020).  Reduced-bias and partially reduced-bias mean-of-order-p value-at-risk estimation: a Monte-Carlo comparison and an application. Journal of Statistical Computation and Simulation. 90, 1735-1752., Number 10 Abstract
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