Comptes Rendus
no. 11
Statistics/Mathematical Analysis
Rates of convergence for nonparametric deconvolution
[Vitesses de convergence en déconvolution nonparamétrique]

Présenté par : Jean-Pierre Kahane

Claire Lacour1
1 Laboratoire MAP 5, Université Paris 5, 45, rue des Saints-Pères, 75270 Paris cedex 06, France
Comptes Rendus. Mathématique, Volume 342 (2006) no. 11, pp. 877-882.

Cette Note présente des vitesses de convergence originales pour le problème de déconvolution. On suppose que la densité estimée ainsi que la densité du bruit sont « supersmooth » et on calcule le risque pour deux types d'estimateurs.

This note presents original rates of convergence for the deconvolution problem. We assume that both the estimated density and noise density are supersmooth and we compute the risk for two kinds of estimators.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.04.006
Claire Lacour 1

1 Laboratoire MAP 5, Université Paris 5, 45, rue des Saints-Pères, 75270 Paris cedex 06, France 
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Claire Lacour. Rates of convergence for nonparametric deconvolution. Comptes Rendus. Mathématique, Volume 342 (2006) no. 11, pp. 877-882. doi : 10.1016/j.crma.2006.04.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.04.006/

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[4] F. Comte, Y. Rozenholc, M.-L. Taupin, Penalized contrast estimator for adaptive density deconvolution, Canad. J. Statist. 34, 2006, in press

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[6] J. Fan On the optimal rates of convergence for nonparametric deconvolution problem, Ann. Statist., Volume 19 (1991), pp. 1257-1272

[7] J. Fan Adaptively local one-dimensional subproblems with application to a deconvolution problem, Ann. Statist., Volume 21 (1993), pp. 600-610

[8] M.C. Liu; R.L. Taylor A consistent non-parametric density estimator for the deconvolution problem, Canad. J. Statist., Volume 17 (1989), pp. 427-438

[9] M. Pensky; B. Vidakovic Adaptive wavelet estimator for nonparametric density deconvolution, Ann. Statist., Volume 27 (1999), pp. 2033-2053

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