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2010 | 30 | 1 | 35-51
Tytuł artykułu

Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation?

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EN
Abstrakty
EN
In this article, we begin with an asymptotic comparison at optimal levels of the so-called "maximum likelihood" (ML) extreme value index estimator, based on the excesses over a high random threshold, denoted PORT-ML, with PORT standing for peaks over random thresholds, with a similar ML estimator, denoted PORT-MP, with MP standing for modified-Pareto. The PORT-MP estimator is based on the same excesses, but with a trial of accommodation of bias on the Generalized Pareto model underlying those excesses. We next compare the behaviour of these ML implicit estimators with the equivalent behaviour of a few explicit tail index estimators, the Hill, the moment, the generalized Hill and the mixed moment. As expected, none of the estimators can always dominate the alternatives, even when we include second-order MVRB tail index estimators, with MVRB standing for minimum-variance reduced-bias. However, the asymptotic performance of the MVRB estimators is quite interesting and provides a challenge for a further study of these MVRB estimators at optimal levels.
Twórcy
  • DEIO and CEAUL, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
  • Instituto Politécnico de Tomar and CEAUL
Bibliografia
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  • [10] M.I. Fraga Alves, M.I. Gomes and L. de Haan, A new class of semi-parametric estimators of the second order parameter, Portugaliae Mathematica 60 (2) (2003), 193-214.
  • [11] M.I. Fraga Alves, M.I. Gomes, L. de Haan and C. Neves, The mixed moment estimator and location invariant alternatives, Extremes, 12 (2009), 149-185.
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  • [14] M.I. Gomes, M.I. Fraga Alves, and P.A. Santos, PORT Hill and Moment Estimators for Heavy-Tailed Models, Commun. Statist. - Simul. & Comput. 37 (2008a), 1281-1306.
  • [15] M.I. Gomes, L. de Haan and L. Henriques-Rodrigues, Tail index estimation through accommodation of bias in the weighted log-excesses, J. Royal Statistical Society B70 (1) (2008b), 31-52.
  • [16] M.I. Gomes and L. Henriques-Rodrigues, Tail index estimation for heavy tails: accommodation of bias in the excesses over a high threshold, Extremes, 11 (3) (2008), 303-328.
  • [17] M.I. Gomes and M.J. Martins, Alternatives to Hill's estimator - asymptotic versus finite sample behaviour, J. Statist. Planning and Inference 93 (2001), 161-180.
  • [18] M.I. Gomes and M.J. Martins, 'Asymptotically unbiased' estimators of the tail index based on external estimation of the second order parameter, Extremes 5 (1) (2002), 5-31.
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  • [20] M.I. Gomes, C. Miranda and C. Viseu, Reduced bias extreme value index estimation and the Jackknife methodology, Statistica Neerlandica 61 (2) (2007) 243-270.
  • [21] M.I. Gomes and C. Neves, Asymptotic comparison of the mixed moment and classical extreme value index estimators, Statistics and Probability Letters 78 (6) (2008), 643-653.
  • [22] M.I. Gomes and D. Pestana, A sturdy reduced-bias extreme quantile (VaR) estimator, J. American Statistical Association 102 (477) (2007), 280-292.
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Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1120
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