Least squares cross-validation for the kernel deconvolution density estimator
[Validation croisée pour l'estimateur à noyau de la déconvolution d'une densité]
Youndjé, Élie1 ; Wells, Martin T.2
1 UMR CNRS 6085, Université de Rouen, 76821 Mont Saint Aignan, France
2 Department of Social Statistics, Cornell University, 364 Ives Hall, Ithaca, NY 14851-0952, USA
Comptes Rendus. Mathématique, Tome 334 (2002) no. 6, pp. 509-513.

En présence d'un échantillon i.i.d. d'une variable aléatoire corrumpue Y=X+ε, avec X et ε indépendants. Nous proposons une méthode basée sur la validation-croisée, pour choisir la largeur de la fenêtre de l'estimateur à noyau de la densité de X. L'optimalité asymptotique de la méthode proposée est établie.

Assume we have i.i.d. replications from the corrupted random variable Y=X+ε, where X and ε are independent. We propose a data-driven bandwidth based on cross-validation ideas, for the kernel deconvolution estimator of the density of X. The proposed method is shown to be asymptotically optimal.

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Accepté le :
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DOI : 10.1016/S1631-073X(02)02291-4
Youndjé, Élie 1 ; Wells, Martin T. 2

1 UMR CNRS 6085, Université de Rouen, 76821 Mont Saint Aignan, France
2 Department of Social Statistics, Cornell University, 364 Ives Hall, Ithaca, NY 14851-0952, USA 
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     title = {Least squares cross-validation for the kernel deconvolution density estimator},
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Youndjé, Élie; Wells, Martin T. Least squares cross-validation for the kernel deconvolution density estimator. Comptes Rendus. Mathématique, Tome 334 (2002) no. 6, pp. 509-513. doi : 10.1016/S1631-073X(02)02291-4. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02291-4/

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