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Extreme Value Index Estimators and Smoothing Alternatives: Review and Simulation Comparison

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  • Tsourti, Zoi
  • Panaretos, John

Abstract

Extreme-value theory and corresponding analysis is an issue extensively applied in many different fields. The central point of this theory is the estimation of a parameter γ, known as extreme-value index. In this paper we review several extreme-value index estimators, ranging from the oldest ones to the most recent developments. Moreover, some smoothing and robustifying procedures of these estimators are presented. A simulation study is conducted in order to compare the behaviour of the estimators and their smoothed alternatives. Maybe, the most prominent result of this study is that no uniformly best estimator exists and that the behaviour of estimators depends on the value of the parameter γ itself

Suggested Citation

  • Tsourti, Zoi & Panaretos, John, 2001. "Extreme Value Index Estimators and Smoothing Alternatives: Review and Simulation Comparison," MPRA Paper 6384, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:6384
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    File URL: https://mpra.ub.uni-muenchen.de/6384/1/MPRA_paper_6384.pdf
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    References listed on IDEAS

    as
    1. Jon Danielsson & Casper G. de Vries, 1998. "Beyond the Sample: Extreme Quantile and Probability Estimation," FMG Discussion Papers dp298, Financial Markets Group.
    2. M. I. Barão & J. A. Tawn, 1999. "Extremal analysis of short series with outliers: sea‐levels and athletics records," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 469-487.
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    Cited by:

    1. Tsourti, Zoi & Panaretos, John, 2004. "Extreme-value analysis of teletraffic data," Computational Statistics & Data Analysis, Elsevier, vol. 45(1), pages 85-103, February.
    2. Mohamed El Ghourabi & Asma Nani & Imed Gammoudi, 2021. "A value‐at‐risk computation based on heavy‐tailed distribution for dynamic conditional score models," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 2790-2799, April.
    3. Imed Gammoudi & Lotfi BelKacem & Mohamed El Ghourabi, 2014. "Value at Risk Estimation for Heavy Tailed Distributions," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 8(3), pages 109-125.

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    More about this item

    Keywords

    Extreme value index; Semi-parametric estimation; Smoothing modification;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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