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On bootstrap sample size in extreme value theory

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  • Geluk, J.L.
  • de Haan, L.F.M.

Abstract

It has been known for a long time that for bootstrapping the probability distribution of the maximum of a sample consistently, the bootstrap sample size needs to be of smaller order than the original sample size. See Jun Shao and Dongsheng Tu (1995), Ex. 3.9,p. 123. We show that the same is true if we use the bootstrap for estimating an intermediate quantile.

Suggested Citation

  • Geluk, J.L. & de Haan, L.F.M., 2002. "On bootstrap sample size in extreme value theory," Econometric Institute Research Papers EI 2002-40, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:541
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    References listed on IDEAS

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    1. Holger Drees, 1998. "On Smooth Statistical Tail Functionals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 187-210, March.
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    Cited by:

    1. Carsten Bormann & Julia Schaumburg & Melanie Schienle, 2016. "Beyond Dimension two: A Test for Higher-Order Tail Risk," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(3), pages 552-580.
    2. Peng, Liang & Qi, Yongcheng, 2008. "Bootstrap approximation of tail dependence function," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1807-1824, September.
    3. Carsten Bormann & Melanie Schienle & Julia Schaumburg, 2014. "A Test for the Portion of Bivariate Dependence in Multivariate Tail Risk," Tinbergen Institute Discussion Papers 14-024/III, Tinbergen Institute, revised 23 Jun 2014.

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    Keywords

    Bootstrap; Regular variation;

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