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Exact convergence rate of bootstrap quantile variance estimator
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  • Published: December 1988

Exact convergence rate of bootstrap quantile variance estimator

  • Peter Hall1 &
  • Michael A. Martin1 

Probability Theory and Related Fields volume 80, pages 261–268 (1988)Cite this article

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

Authors
  1. Peter Hall
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  2. Michael A. Martin
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Cite this article

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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