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2010 | 30 | 1 | 5-19
Tytuł artykułu

An asymptotically unbiased moment estimator of a negative extreme value index

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Języki publikacji
EN
Abstrakty
EN
In this paper 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.
Twórcy
  • DM and CMA, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal
  • DEIO and CEAUL, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
Bibliografia
  • [1] F. Caeiro, M.I. Gomes and D.D. Pestana, Direct reduction of bias of the classical Hill estimator, Revstat 3 (2) (2005), 113-136.
  • [2] A.L.M. Dekkers, J.H.J. Einmahl and L. de Haan, A moment estimator for the index of an extreme-value distribution, The Annals of Statistics 17 (4) (1989), 1833-1855.
  • [3]G. Draisma, L. de Haan, L. Peng and T. Themido Pereira, A bootstrap-based method to achieve optimality in estimating the extreme value index, Extremes 2 (4) (1999), 367-404.
  • [4] M.I. Fraga Alves, Weiss-Hill estimator, Test 10 (2001), 203-224.
  • [5] B.V. Gnedenko, Sur la distribution limite du terme maximum d'une série aléatoire, Ann. Math. 44 (1943), 423-453.
  • [6] M.I. Gomes, L. de Haan and L. Henriques Rodrigues, Tail Index estimation for heavy-tailed models: accommodation of bias in weighted log-excesses, J. R. Stat. Soc. Ser. B 70 (1) (2008), 31-52.
  • [7] M.I. Gomes, M.J. Martins and M.M. Neves, Improving second order reduced-bias tail index estimation, Revstat 5 (2) (2007), 177-207.
  • [8] M.I. Gomes and C. Neves, Asymptotic comparison of the mixed moment and classical extreme value index estimators, Statistics & Probability Letters 78 (2008), 643-653.
  • [9] M.I. Gomes and O. Oliveira, The bootstrap methodology in Statistics of Extremes - choice of the optimal sample fraction, Extremes 4 (4) (2001), 331-358.
  • [10] L. de Haan, On Regular Variation and its Application to the Weak Convergence of Sample Extremes, Mathematical Centre Tract 32, Amesterdam 1970.
  • [11] L. de Haan and A. Ferreira, Extreme Value Theory: an Introduction, Springer, LLC New York 2006.
  • [12] B.M. Hill, A Simple General Approach to Inference About the Tail of a Distribution, The Annals of Statistics 3 (5) (1975), 1163-1174.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1118
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