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Convergence rates in density estimation for data from infinite-order moving average processes
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  • Published: June 1990

Convergence rates in density estimation for data from infinite-order moving average processes

  • Peter Hall1 &
  • Jeffrey D. Hart2 

Probability Theory and Related Fields volume 87, pages 253–274 (1990)Cite this article

  • 173 Accesses

  • 53 Citations

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Summary

The effect of long-range dependence in nonparametric probability density estimation is investigated under the assumption that the observed data are a sample from a stationary, infinite-order moving average process. It is shown that to first order, the mean integrated squared error (MISE) of a kernel estimator for moving average data may be expanded as the sum of MISE of the kernel estimator for a same-sizerandom sample, plus a term proportional to the variance of the moving average sample mean. The latter term does not depend on bandwidth, and so imposes a ceiling on the convergence rate of a kernel estimator regardless of how bandwidth is chosen. This ceiling can be quite significant in the case of long-range dependence. We show thatall density estimators have the convergence rate ceiling possessed by kernel estimators.

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Author information

Authors and Affiliations

  1. Department of Statistics, Faculty of Economics and Commerce, Australian National University, GPO Box 4, 2601, Canberra, ACT, Australia

    Peter Hall

  2. Department of Statistics, Texas A&M University, 77843, College Station, TX, USA

    Jeffrey D. Hart

Authors
  1. Peter Hall
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  2. Jeffrey D. Hart
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Additional information

The research of Dr. Hart was done while he was visiting the Australian National University, and was supported in part by ONR Contract N00014-85-K-0723

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Cite this article

Hall, P., Hart, J.D. Convergence rates in density estimation for data from infinite-order moving average processes. Probab. Th. Rel. Fields 87, 253–274 (1990). https://doi.org/10.1007/BF01198432

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  • Received: 27 July 1989

  • Revised: 18 June 1990

  • Issue Date: June 1990

  • DOI: https://doi.org/10.1007/BF01198432

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Keywords

  • Probability Density
  • Stochastic Process
  • Probability Theory
  • Convergence Rate
  • Average Data
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