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On some representations of the Bootstrap
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  • Published: August 1989

On some representations of the Bootstrap

  • Shaw-Hwa Lo1 

Probability Theory and Related Fields volume 82, pages 411–418 (1989)Cite this article

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  • 6 Citations

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Summary

The bootstrap statistic \(\hat \theta _n^* - \hat \theta _n \) is represented as the sum of two terms, one of which has the same distribution as \(\hat \theta _n - \theta \) and the other is a relatively negligible remainder. The representation is then applied to the problems of estimating a distribution and a quantile. The study includes the tail part of the distribution and quantiles for which the convergence rates could be faster than the usual “n -1/2” rate.

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References

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Author information

Authors and Affiliations

  1. Department of Statistics, Harvard University, 1 Oxford Street, 02138, Cambridge, Ma, USA

    Shaw-Hwa Lo

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  1. Shaw-Hwa Lo
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Lo, SH. On some representations of the Bootstrap. Probab. Th. Rel. Fields 82, 411–418 (1989). https://doi.org/10.1007/BF00339995

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  • Received: 04 November 1988

  • Issue Date: August 1989

  • DOI: https://doi.org/10.1007/BF00339995

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Keywords

  • Stochastic Process
  • Probability Theory
  • Convergence Rate
  • Statistical Theory
  • Tail Part
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