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Smoothed cross-validation
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  • Published: March 1992

Smoothed cross-validation

  • Peter Hall1,2,
  • J. S. Marron1,2 &
  • Byeong U. Park1,2 

Probability Theory and Related Fields volume 92, pages 1–20 (1992)Cite this article

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Summary

For bandwidth selection of a kernel density estimator, a generalization of the widely studied least squares cross-validation method is considered. The essential idea is to do a particular type of “presmoothing” of the data. This is seen to be essentially the same as using the smoothed bootstrap estimate of the mean integrated squared error. Analysis reveals that a rather large amount of presmoothing yields excellent asymptotic performance. The rate of convergence to the optimum is known to be best possible under a wide range of smoothness conditions. The method is more appealing than other selectors with this property, because its motivation is not heavily dependent on precise asymptotic analysis, and because its form is simple and intuitive. Theory is also given for choice of the amount of presmoothing, and this is used to derive a data-based method for this choice.

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Author information

Authors and Affiliations

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

    Peter Hall, J. S. Marron & Byeong U. Park

  2. Seoul National University, Korea

    Peter Hall, J. S. Marron & Byeong U. Park

Authors
  1. Peter Hall
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  2. J. S. Marron
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  3. Byeong U. Park
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Additional information

Research of the second author was done while on leave from the University of North Carolina. That of both the second and third was partially supported by National Science Foundation Grants DMS-8701201 and DMS-8902973

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Hall, P., Marron, J.S. & Park, B.U. Smoothed cross-validation. Probab. Th. Rel. Fields 92, 1–20 (1992). https://doi.org/10.1007/BF01205233

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  • Received: 10 May 1990

  • Revised: 27 March 1991

  • Issue Date: March 1992

  • DOI: https://doi.org/10.1007/BF01205233

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Asymptotic Analysis
  • Kernel Density
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