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Variable window width kernel estimates of probability densities
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  • Published: December 1988

Variable window width kernel estimates of probability densities

  • Peter Hall1 &
  • J. S. Marron1 nAff2 

Probability Theory and Related Fields volume 80, pages 37–49 (1988)Cite this article

  • 363 Accesses

  • 66 Citations

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Abstract

Kernel density estimators which allow different amounts of smoothing at different locations are studied. Modifications of estimators proposed by Breiman, Meisel and Purcell (1977) and Abramson (1982a), which have variable window widths, are seen to have very fast rates of convergence. These rates have traditionally been obtained using a less natural higher order kernel, which has the disadvantage of allowing an estimator which takes on negative values.

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References

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Author information

Author notes
  1. J. S. Marron

    Present address: Department of Statistics, University of North Carolina, 27514, Chapel Hill, NC, USA

Authors and Affiliations

  1. Australian National University, P.O. Box 4, 2600, Canberra, ACT, Australia

    Peter Hall & J. S. Marron

Authors
  1. Peter Hall
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  2. J. S. Marron
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Additional information

Research partially supported by NSF Grants DMS-8400602 and DMS-8701201

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Cite this article

Hall, P., Marron, J.S. Variable window width kernel estimates of probability densities. Probab. Th. Rel. Fields 80, 37–49 (1988). https://doi.org/10.1007/BF00348751

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  • Received: 20 December 1986

  • Revised: 26 May 1988

  • Issue Date: December 1988

  • DOI: https://doi.org/10.1007/BF00348751

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Keywords

  • Probability Density
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Fast Rate
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