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Consistency of full-sample bootstrap for estimating high-quantile, tail probability, and tail index

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  • Svetlana Litvinova
  • Mervyn J. Silvapulle

Abstract

We show that the full-sample bootstrap is asymptotically valid for constructing confidence intervals for high-quantiles, tail probabilities, and other tail parameters of a univariate distribution. This resolves the doubts that have been raised about the validity of such bootstrap methods. In our extensive simulation study, the overall performance of the bootstrap method was better than that of the standard asymptotic method, indicating that the bootstrap method is at least as good, if not better than, the asymptotic method for inference. This paper also lays the foundation for developing bootstrap methods for inference about tail events in multivariate statistics; this is particularly important because some of the non-bootstrap methods are complex.

Suggested Citation

  • Svetlana Litvinova & Mervyn J. Silvapulle, 2020. "Consistency of full-sample bootstrap for estimating high-quantile, tail probability, and tail index," Monash Econometrics and Business Statistics Working Papers 15/20, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2020-15
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    File URL: https://www.monash.edu/business/ebs/research/publications/ebs/wp15-2020.pdf
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    References listed on IDEAS

    as
    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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    More about this item

    Keywords

    full-sample bootstrap; intermediate order statistic; extreme value index; Hill estimator; tail probability; tail quantile;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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