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Estimation of Convolution In The Model with Noise

Author

Listed:
  • Christophe Chesneau

    (LMNO, Université de Caen Basse-Normandie Département de Mathématiques et UFR de Sciences)

  • Fabienne Comte

    (MAP5, UMR CNRS 8145, Université Paris Descartes, Sorbonne Paris Cité)

  • Gwennaëlle Mabon

    (CREST)

  • Fabien Navarro

    (Université de Nantes, Laboratoire de Mathématiques Jean Leray UFR Sciences et Techniques)

Abstract

We investigate the estimation of the ?-fold convolution of the density of an unob- served variable X from n i.i.d. observations of the convolution model Y = X + ?. We first assume that the density of the noise ? is known and define nonadaptive estimators, for which we provide bounds for the mean integrated squared error (MISE). In particular, under some smoothness assumptions on the densities of X and ?, we prove that the parametric rate of con-vergence 1/n can be attained. Then we construct an adaptive estimator using a penalization approach having similar performances to the nonadaptive one. The price for its adaptivity is a logarithmic term. The results are extended to the case of unknown noise density, under the condition that an independent noise sample is available. Lastly, we report a simulation study to support our theoretical findings.

Suggested Citation

  • Christophe Chesneau & Fabienne Comte & Gwennaëlle Mabon & Fabien Navarro, 2014. "Estimation of Convolution In The Model with Noise," Working Papers 2014-39, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2014-39
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    References listed on IDEAS

    as
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