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Semiparametric Density Deconvolution

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  • MARTIN L. HAZELTON
  • BERWIN A. TURLACH

Abstract

. A new semiparametric method for density deconvolution is proposed, based on a model in which only the ratio of the unconvoluted to convoluted densities is specified parametrically. Deconvolution results from reweighting the terms in a standard kernel density estimator, where the weights are defined by the parametric density ratio. We propose that in practice, the density ratio be modelled on the log‐scale as a cubic spline with a fixed number of knots. Parameter estimation is based on maximization of a type of semiparametric likelihood. The resulting asymptotic properties for our deconvolution estimator mirror the convergence rates in standard density estimation without measurement error when attention is restricted to our semiparametric class of densities. Furthermore, numerical studies indicate that for practical sample sizes our weighted kernel estimator can provide better results than the classical non‐parametric kernel estimator for a range of densities outside the specified semiparametric class.

Suggested Citation

  • Martin L. Hazelton & Berwin A. Turlach, 2010. "Semiparametric Density Deconvolution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 91-108, March.
    • Handle: RePEc:bla:scjsta:v:37:y:2010:i:1:p:91-108
    DOI: 10.1111/j.1467-9469.2009.00669.x
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    References listed on IDEAS

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    4. Bert Van Es & Hae‐Won Uh, 2005. "Asymptotic Normality of Kernel‐Type Deconvolution Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 467-483, September.
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    7. Raymond J. Carroll & Peter Hall, 2004. "Low order approximations in deconvolution and regression with errors in variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 31-46, February.
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    Cited by:

    1. Roy, Arkaprava & Sarkar, Abhra, 2023. "Bayesian semiparametric multivariate density deconvolution via stochastic rotation of replicates," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).

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