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Using a Bootstrap Method to choose the Sample Fraction in Tail Index Estimation

Author

Listed:
  • J. Danielsson

    (University of Iceland)

  • L. de Haan

    (Erasmus University Rotterdam)

  • L. Peng

    (Erasmus University Rotterdam)

  • C.G. de Vries

    (Erasmus University Rotterdam)

Abstract

We use a subsample bootstrap method to get a consistent estimate of the asymptotically optimal choice of the samplefraction, in the sense of minimal mean squared error, which is needed for tail index estimation. Unlike previous methodsour procedure is fully self contained. In particular, the method is not conditional on an initial consistent estimate of the tailindex; and the ratio of the first and second order tail indices is left unrestricted, but we require the ratio to be strictlypositive. Hence the current method yields a complete solution to tail index estimation as it is not predicated on a more orless arbitrary choice of the number of highest order statistics.

Suggested Citation

  • J. Danielsson & L. de Haan & L. Peng & C.G. de Vries, 1997. "Using a Bootstrap Method to choose the Sample Fraction in Tail Index Estimation," Tinbergen Institute Discussion Papers 97-016/4, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:19970016
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    References listed on IDEAS

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    3. 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.
    4. de Haan, L. & Pereira, T. Themido, 1999. "Estimating the index of a stable distribution," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 39-55, January.
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