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Estimation of convolution in the model with noise

Author

Listed:
  • C. Chesneau
  • F. Comte
  • G. Mabon
  • F. Navarro

Abstract

We investigate the estimation of the ℓ-fold convolution of the density of an unobserved variable X from n i.i.d. observations of the convolution model . We first assume that the density of the noise ϵ is known and define non-adaptive estimators, for which we provide bounds for the mean integrated squared error. In particular, under some smoothness assumptions on the densities of X and ϵ , we prove that the parametric rate of convergence can be attained. Then, we construct an adaptive estimator using a penalisation approach having similar performances to the non-adaptive 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

  • C. Chesneau & F. Comte & G. Mabon & F. Navarro, 2015. "Estimation of convolution in the model with noise," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 286-315, September.
    • Handle: RePEc:taf:gnstxx:v:27:y:2015:i:3:p:286-315
    DOI: 10.1080/10485252.2015.1041944
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