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Reduced‐bias tail index estimation and the jackknife methodology

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  • M. Ivette Gomes
  • Cristina Miranda
  • Clara Viseu

Abstract

In the context of regularly varying tails, we first analyze a generalization of the classical Hill estimator of a positive tail index, with members that are not asymptotically more efficient than the original one. This has led us to propose alternative classical tail index estimators, that may perform asymptotically better than the Hill estimator. As the improvement is not really significant, we also propose generalized jackknife estimators based on any two members of these two classes. These generalized jackknife estimators are compared with the Hill estimator and other reduced‐bias estimators available in the literature, asymptotically, and for finite samples, through the use of Monte Carlo simulation. The finite‐sample behaviour of the new reduced‐bias estimators is also illustrated through a practical example in the field of finance.

Suggested Citation

  • M. Ivette Gomes & Cristina Miranda & Clara Viseu, 2007. "Reduced‐bias tail index estimation and the jackknife methodology," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(2), pages 243-270, May.
    • Handle: RePEc:bla:stanee:v:61:y:2007:i:2:p:243-270
    DOI: 10.1111/j.1467-9574.2007.00346.x
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    Cited by:

    1. Cai, J., 2012. "Estimation concerning risk under extreme value conditions," Other publications TiSEM a92b089f-bc4c-41c2-b297-c, Tilburg University, School of Economics and Management.
    2. 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.
    3. 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.
    4. Yves Dominicy & Pauliina Ilmonen & David Veredas, 2017. "Multivariate Hill Estimators," International Statistical Review, International Statistical Institute, vol. 85(1), pages 108-142, April.
    5. Gomes, M. Ivette & Hall, Andreia & Miranda, M. Cristina, 2008. "Subsampling techniques and the Jackknife methodology in the estimation of the extremal index," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2022-2041, January.

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