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A New Class of Reduced-Bias Generalized Hill Estimators

Author

Listed:
  • Lígia Henriques-Rodrigues

    (School of Science and Technology and Research Center in Mathematics and Applications (CIMA), University of Évora, 7000-671 Évora, Portugal
    These authors contributed equally to this work.)

  • Frederico Caeiro

    (NOVA School of Science and Technology (NOVA FCT) and Center for Mathematics and Applications (CMA), NOVA University Lisbon, 2829-516 Caparica, Portugal
    These authors contributed equally to this work.)

  • M. Ivette Gomes

    (Department of Statistics and Operational Research (DEIO), Faculty of Sciences of the University of Lisbon (FCUL) and Centre of Statistics and its Applications (CEAUL), University of Lisbon (ULisboa), 1749-016 Lisbon, Portugal
    These authors contributed equally to this work.)

Abstract

The estimation of the extreme value index (EVI) is a crucial task in the field of statistics of extremes, as it provides valuable insights into the tail behavior of a distribution. For models with a Pareto-type tail, the Hill estimator is a popular choice. However, this estimator is susceptible to bias, which can lead to inaccurate estimations of the EVI, impacting the reliability of risk assessments and decision-making processes. This paper introduces a novel reduced-bias generalized Hill estimator, which aims to enhance the accuracy of EVI estimation by mitigating the bias.

Suggested Citation

  • Lígia Henriques-Rodrigues & Frederico Caeiro & M. Ivette Gomes, 2024. "A New Class of Reduced-Bias Generalized Hill Estimators," Mathematics, MDPI, vol. 12(18), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2866-:d:1478401
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    References listed on IDEAS

    as
    1. Gomes, M. Ivette & Pestana, Dinis, 2007. "A Sturdy Reduced-Bias Extreme Quantile (VaR) Estimator," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 280-292, March.
    2. 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.
    3. 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.
    4. Jan Beran & Dieter Schell & Milan Stehlík, 2014. "The harmonic moment tail index estimator: asymptotic distribution and robustness," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 193-220, February.
    5. 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.
    6. L. De Haan & L. Peng, 1998. "Comparison of tail index estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(1), pages 60-70, March.
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