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Exact convergence rate of bootstrap quantile variance estimator

  • Published: December 1988
  • Volume 80, pages 261–268, (1988)
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Exact convergence rate of bootstrap quantile variance estimator
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  • Peter Hall1 &
  • Michael A. Martin1 
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Summary

It is shown that the relative error of the bootstrap quantile variance estimator is of precise order n -1/4, when n denotes sample size. Likewise, the error of the bootstrap sparsity function estimator is of precise order n -1/4. Therefore as point estimators these estimators converge more slowly than the Bloch-Gastwirth estimator and kernel estimators, which typically have smaller error of order at most n -2/5.

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Authors and Affiliations

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

    Peter Hall & Michael A. Martin

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  1. Peter Hall
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  2. Michael A. Martin
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Hall, P., Martin, M.A. Exact convergence rate of bootstrap quantile variance estimator. Probab. Th. Rel. Fields 80, 261–268 (1988). https://doi.org/10.1007/BF00356105

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  • Received: 20 November 1987

  • Revised: 07 July 1988

  • Issue Date: December 1988

  • DOI: https://doi.org/10.1007/BF00356105

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Keywords

  • Relative Error
  • Stochastic Process
  • Probability Theory
  • Convergence Rate
  • Mathematical Biology
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