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Competitive estimation of the extreme value index

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  • Gomes, M. Ivette
  • Henriques-Rodrigues, Lígia

Abstract

The mean-of-order-p (MOp) extreme value index (EVI) estimators are based on Hölder’s mean of an adequate set of statistics, and generalize the classical Hill EVI-estimators, associated with p=0. Such a class of estimators, dependent on the tuning parameter p∈R, has revealed to be highly flexible, but it is not invariant for changes in location. To make the MOp location-invariant, it is thus sensible to use the peaks over a random threshold (PORT) methodology, based upon the excesses over an adequate ascending order statistic. In this article, apart from an asymptotic comparison at optimal levels of the optimal MOp class and some competitive EVI-estimators, like a Pareto probability weighted moments EVI-estimator, a few details on PORT classes of EVI-estimators are provided, enhancing their high efficiency both asymptotically and for finite samples.

Suggested Citation

  • Gomes, M. Ivette & Henriques-Rodrigues, Lígia, 2016. "Competitive estimation of the extreme value index," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 128-135.
    • Handle: RePEc:eee:stapro:v:117:y:2016:i:c:p:128-135
    DOI: 10.1016/j.spl.2016.05.012
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    References listed on IDEAS

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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. Frederico Caeiro & M. Ivette Gomes & Björn Vandewalle, 2014. "Semi-Parametric Probability-Weighted Moments Estimation Revisited," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 1-29, March.
    3. Dekkers, A. L. M. & Dehaan, L., 1993. "Optimal Choice of Sample Fraction in Extreme-Value Estimation," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 173-195, November.
    4. M. Ivette Gomes & Armelle Guillou, 2015. "Extreme Value Theory and Statistics of Univariate Extremes: A Review," International Statistical Review, International Statistical Institute, vol. 83(2), pages 263-292, August.
    5. M. Ivette Gomes & Laurens De Haan & Lígia Henriques Rodrigues, 2008. "Tail index estimation for heavy‐tailed models: accommodation of bias in weighted log‐excesses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 31-52, February.
    6. 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.
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    Cited by:

    1. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.

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