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Parametrically Assisted Nonparametric Estimation of a Density in the Deconvolution Problem

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  • Aurore Delaigle
  • Peter Hall

Abstract

Nonparametric estimation of a density from contaminated data is a difficult problem, for which convergence rates are notoriously slow. We introduce parametrically assisted nonparametric estimators which can dramatically improve on the performance of standard nonparametric estimators when the assumed model is close to the true density, without degrading much the quality of purely nonparametric estimators in other cases. We establish optimal convergence rates for our problem and discuss estimators that attain these rates. The very good numerical properties of the methods are illustrated via a simulation study. Supplementary materials for this article are available online.

Suggested Citation

  • Aurore Delaigle & Peter Hall, 2014. "Parametrically Assisted Nonparametric Estimation of a Density in the Deconvolution Problem," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 717-729, June.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:506:p:717-729
    DOI: 10.1080/01621459.2013.857611
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    Cited by:

    1. Cornelis J. Potgieter, 2020. "Density deconvolution for generalized skew-symmetric distributions," Journal of Statistical Distributions and Applications, Springer, vol. 7(1), pages 1-20, December.
    2. Ali Al-Sharadqah & Majid Mojirsheibani & William Pouliot, 2020. "On the performance of weighted bootstrapped kernel deconvolution density estimators," Statistical Papers, Springer, vol. 61(4), pages 1773-1798, August.

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