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Extreme Value Index Estimators and Smoothing Alternatives: A Critical Review

Author

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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 the 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.

Suggested Citation

  • Tsourti, Zoi & Panaretos, John, 2003. "Extreme Value Index Estimators and Smoothing Alternatives: A Critical Review," MPRA Paper 6390, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:6390
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    File URL: https://mpra.ub.uni-muenchen.de/6390/1/MPRA_paper_6390.pdf
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    References listed on IDEAS

    as
    1. Armelle Guillou & Peter Hall, 2001. "A diagnostic for selecting the threshold in extreme value analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 293-305.
    2. 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.
    3. 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.
    4. Jón Daníelsson & Casper G. de Vries, 1998. "Beyond the Sample: Extreme Quantile and Probability Estimation," Tinbergen Institute Discussion Papers 98-016/2, Tinbergen Institute.
    5. Olivier V. Pictet & Michel M. Dacorogna & Ulrich A. Muller, 1996. "Hill, Bootstrap and Jackknife Estimators for Heavy Tails," Working Papers 1996-12-10, Olsen and Associates.
    6. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    7. Peng, L., 1998. "Asymptotically unbiased estimators for the extreme-value index," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 107-115, June.
    8. 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.
    9. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 27(01), pages 117-137, May.
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    Citations

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    Cited by:

    1. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.

    More about this item

    Keywords

    Extreme value index; Semi-parametric estimation; Smoothing modification;

    JEL classification:

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

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