Estimation of Convolution In The Model with Noise

Christophe Chesneau (), Fabienne Comte (), Gwennaëlle Mabon () and Fabien Navarro ()
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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

No 2014-39, Working Papers from Center for Research in Economics and Statistics

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.

Keywords: Adaptive; estimation.; Convolution; of; densities.; Measurement; errors.; Oracle; inequality.; Nonparametric; estimator. (search for similar items in EconPapers)
Pages: 27
Date: 2014-06
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