Probability Theory and Related Fields

, Volume 80, Issue 2, pp 261–268

Exact convergence rate of bootstrap quantile variance estimator

  • Peter Hall
  • Michael A. Martin

DOI: 10.1007/BF00356105

Cite this article as:
Hall, P. & Martin, M.A. Probab. Th. Rel. Fields (1988) 80: 261. doi:10.1007/BF00356105


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.

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Peter Hall
    • 1
  • Michael A. Martin
    • 1
  1. 1.Department of StatisticsAustralian National UniversityCanberraAustralia

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