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Performance of balanced bootstrap resampling in distribution function and quantile problems
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  • Published: June 1990

Performance of balanced bootstrap resampling in distribution function and quantile problems

  • Peter Hall1 

Probability Theory and Related Fields volume 85, pages 239–260 (1990)Cite this article

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  • 10 Citations

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Summary

It is shown that balanced resampling improves on ordinary uniform resampling when employed to estimate distribution functions or quantiles, but that the improvement is not by an order of magnitude as happens in problems such as bias estimation. Maximum improvement occurs at the centre of the distribution, where performance increases by 175%. The increase is only 16% at the 2.5% and 97.5% quantiles. In general the improvement is by the factor {1−φ2(1−Φ)Φ}−1, where Φ is the standard normal distribution function and φ=Φ′.

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Authors and Affiliations

  1. Department of Statistics, The Australian National University, GPO Box 4, 2601, Canberra, AGT, Australia

    Peter Hall

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  1. Peter Hall
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Cite this article

Hall, P. Performance of balanced bootstrap resampling in distribution function and quantile problems. Probab. Th. Rel. Fields 85, 239–260 (1990). https://doi.org/10.1007/BF01277983

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  • Received: 22 November 1988

  • Revised: 01 September 1989

  • Issue Date: June 1990

  • DOI: https://doi.org/10.1007/BF01277983

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Keywords

  • Distribution Function
  • Normal Distribution
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
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