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Simple kernel estimators for certain nonparametric deconvolution problems

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  • van Es, A. J.
  • Kok, A. R.

Abstract

We consider deconvolution problems where the observations are equal in distribution to X = [lambda]1E1 + ... + [lambda]mEm + Y, or to X = [mu]1L1 + ... + [mu]mLm + Y. Here the random variables in the sums are independent, the Ei are exponentially distributed, the Li are Laplace distributed and Y has an unknown distribution F which we want to estimate. The constants [lambda]i and [mu]i are given. These problems include exponential, gamma and Laplace deconvolution. We derive inversion formulas, expressing F in terms of the distribution of the observations. Simple kernel estimators of F and its density f are then introduced by plugging in standard kernel estimators of the distribution of the observations. The pointwise asymptotic properties of the estimators are investigated.

Suggested Citation

  • van Es, A. J. & Kok, A. R., 1998. "Simple kernel estimators for certain nonparametric deconvolution problems," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 151-160, August.
    • Handle: RePEc:eee:stapro:v:39:y:1998:i:2:p:151-160
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    References listed on IDEAS

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    1. Masry, E., 1993. "Asymptotic Normality for Deconvolution Estimators of Multivariate Densities of Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 47-68, January.
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    Cited by:

    1. 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.
    2. van Es, Bert & Gugushvili, Shota, 2008. "Weak convergence of the supremum distance for supersmooth kernel deconvolution," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2932-2938, December.
    3. Holzmann, Hajo & Bissantz, Nicolai & Munk, Axel, 2007. "Density testing in a contaminated sample," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 57-75, January.

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    Keywords

    Deconvolution Kernel estimation;

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