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A Bootstrap-based Method to Achieve Optimality in Estimating the Extreme-value Index

Author

Listed:
  • Laurens F.M. de Haan
  • Liang Peng

    (Erasmus University Rotterdam)

  • T.T. Pereira

    (University of Lisbon)

Abstract

Estimators of the extreme-value index are based on a set of upper order statistics. We present an adaptivemethod to choose the number of order statistics involved in an optimal way, balancing variance and biascomponents. Recently this has been achieved for the similar but somewhat less involved case of regularlyvarying tails (Drees and Kaufmann (1997); Danielsson et al.(1997)). The present paper follows the line ofproof of the last paper.

Suggested Citation

  • Laurens F.M. de Haan & Liang Peng & T.T. Pereira, 1997. "A Bootstrap-based Method to Achieve Optimality in Estimating the Extreme-value Index," Tinbergen Institute Discussion Papers 97-099/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:19970099
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    References listed on IDEAS

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    1. 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.
    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. de Haan, L. & Peng, L., 1997. "Rates of Convergence for Bivariate Extremes," Journal of Multivariate Analysis, Elsevier, vol. 61(2), pages 195-230, May.
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    Cited by:

    1. Holger Drees & Laurens F.M. de Haan & Sidney Resnick, 1998. "How to make a Hill Plot," Tinbergen Institute Discussion Papers 98-090/4, Tinbergen Institute.
    2. Peng, L., 1998. "Asymptotically unbiased estimators for the extreme-value index," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 107-115, June.

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