# Data driven density estimation in presence of unknown convolution operator

Abstract : We study the following model of deconvolution $Y=X+\varepsilon$ with i.i.d. observations $Y_1,\dots, Y_n$ and $\varepsilon_{-1},\dots,\varepsilon_{-M}$. The $(X_j)_{1\leq j\leq n}$ are i.i.d. with density $f$, independent of the $\varepsilon_j$. The aim of the paper is to estimate $f$ without knowing the density $f_{\varepsilon}$ of the $\varepsilon_j$. We first define a projection estimator, for which we provide bounds for the pointwise and the integrated $L^2$-risk. We consider ordinary smooth and supersmooth noise $\varepsilon$ with regard to ordinary smooth and supersmooth densities $f$. Then we present an adaptive estimator of the density of $f$. This estimator is obtained by penalization of the projection contrast, which provides model selection. Lastly, we present simulation experiments to illustrate the good performances of our estimator and study from the empirical point of view the importance of theoretical constraints.
Mots-clés :
Type de document :
Article dans une revue
Journal of the Royal Statistical Society: Series B, Royal Statistical Society, 2011, 73 (4), pp.601-627. 〈10.1111/j.1467-9868.2011.00775.x〉
Domaine :
Liste complète des métadonnées

Littérature citée [28 références]

https://hal.archives-ouvertes.fr/hal-00317447
Contributeur : Fabienne Comte <>
Soumis le : vendredi 14 novembre 2008 - 16:46:17
Dernière modification le : jeudi 31 mai 2018 - 09:12:01
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 10:48:43

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### Citation

Fabienne Comte, Claire Lacour. Data driven density estimation in presence of unknown convolution operator. Journal of the Royal Statistical Society: Series B, Royal Statistical Society, 2011, 73 (4), pp.601-627. 〈10.1111/j.1467-9868.2011.00775.x〉. 〈hal-00317447v2〉

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