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Asymptotic comparison of the mixed moment and classical extreme value index estimators

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  • Gomes, M. Ivette
  • Neves, Cláudia

Abstract

A new promising extreme value index estimator, the mixed-moment (MM) estimator, has been recently introduced in the literature. This estimator uses not only the first moment of the top excesses of the log-observations in the sample, the basis of the classical Hill and moment estimators, but also the first moment of another type of statistics, dependent on quotients of top order statistics. In this paper we shall compare, asymptotically at optimal levels, the MM estimator with the classical Hill, the moment and the usually denoted "maximum likelihood" extreme value index estimator, associated to an approximation for the excesses over a high observation provided by the generalized Pareto distribution. Again, the MM estimator cannot always dominate the alternatives, but its asymptotic performance is quite interesting.

Suggested Citation

  • Gomes, M. Ivette & Neves, Cláudia, 2008. "Asymptotic comparison of the mixed moment and classical extreme value index estimators," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 643-653, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:6:p:643-653
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    1. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
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    1. Fátima Brilhante, M. & Ivette Gomes, M. & Pestana, Dinis, 2013. "A simple generalisation of the Hill estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 518-535.
    2. Ivanilda Cabral & Frederico Caeiro & M. Ivette Gomes, 2022. "On the comparison of several classical estimators of the extreme value index," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(1), pages 179-196, January.
    3. Evandro Konzen & Cláudia Neves & Philip Jonathan, 2021. "Modeling nonstationary extremes of storm severity: Comparing parametric and semiparametric inference," Environmetrics, John Wiley & Sons, Ltd., vol. 32(4), June.
    4. Gomes, M. Ivette & Henriques-Rodrigues, Lígia, 2016. "Competitive estimation of the extreme value index," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 128-135.

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