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Bootstrapping the distance between smooth bootstrap and sample quantile distribution
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  • Published: June 1989

Bootstrapping the distance between smooth bootstrap and sample quantile distribution

  • M. Falk1 &
  • R. -D. Reiss1 

Probability Theory and Related Fields volume 82, pages 177–186 (1989)Cite this article

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  • 11 Citations

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Summary

The normalized Kolmogorov-Smirnov and variational distance between the distribution of the sampleq-quantile and the pertaining smooth bootstrap distribution are asymptotically distributed like the absolute value of a normal random variable. The distribution functions of these random distances may serve as measures of the accuracy of the bootstrap procedure.

It is shown that these distribution functions of random distances, and thus the accuracy of the bootstrap procedure, can again consistently be estimated by means of the bootstrap technique.

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References

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Authors and Affiliations

  1. Department of Mathematics, University of Siegen, Hölderlinstrasse 3, D-5900, Siegen 21, Federal Republic of Germany

    M. Falk & R. -D. Reiss

Authors
  1. M. Falk
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  2. R. -D. Reiss
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Cite this article

Falk, M., Reiss, R.D. Bootstrapping the distance between smooth bootstrap and sample quantile distribution. Probab. Th. Rel. Fields 82, 177–186 (1989). https://doi.org/10.1007/BF00354758

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  • Received: 01 June 1988

  • Revised: 23 February 1989

  • Issue Date: June 1989

  • DOI: https://doi.org/10.1007/BF00354758

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Keywords

  • Distribution Function
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Variational Distance
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