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Uniform consistency of automatic and location-adaptive delta-sequence estimators
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  • Published: February 1989

Uniform consistency of automatic and location-adaptive delta-sequence estimators

  • Deborah Nolan1 &
  • J. Stephen Marron2 

Probability Theory and Related Fields volume 80, pages 619–632 (1989)Cite this article

  • 139 Accesses

  • 15 Citations

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Summary

The class of delta-sequence estimators for a probability density includes the kernel, histogram and orthogonal series types, because each can be characterized as a collection of averages of some function that is indexed by a smoothing parameter. There are two important extensions of this class. The first allows a random smoothing parameter, for example that specified by a cross-validation method. The second allows the smoothing parameter to be a function of location, for example an estimator based on nearest-neighbor distance. In this paper a general method is presented which establishes uniform consistency for all of these estimators.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of California, 94720, Berkeley, CA

    Deborah Nolan

  2. Department of Statistics, University of North Carolina, 27514, Chapel Hill, NC

    J. Stephen Marron

Authors
  1. Deborah Nolan
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  2. J. Stephen Marron
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Additional information

Research partially supported by AFOSR Grant No. S-49620-82-C-0144, and by NSF Grant DMS-850-3347

Research supported by NSF Grant DMS-8400602

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Cite this article

Nolan, D., Marron, J.S. Uniform consistency of automatic and location-adaptive delta-sequence estimators. Probab. Th. Rel. Fields 80, 619–632 (1989). https://doi.org/10.1007/BF00318909

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  • Received: 13 March 1987

  • Revised: 20 July 1988

  • Issue Date: February 1989

  • DOI: https://doi.org/10.1007/BF00318909

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Keywords

  • Probability Density
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Smoothing Parameter
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