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Comptes Rendus Mathématique
Volume 334, n° 7
pages 591-595 (2002)
Doi : S1631-073X(02)02298-7
Received : 21 November 2001 ;  accepted : 29 January 2002
Estimation localement suroptimale et adaptative de la densité
Locally superoptimal and adaptive projection density estimators

Denis Bosq
74, rue Dunois, 75013 Paris, France 

Note présentée par Paul Deheuvels


On étudie une version tronquée de l'estimateur par projection dans un cadre général. On montre que cet estimateur atteint une vitesse suroptimale sur un ensemble dense dans la classe des densités à estimer et une vitesse quasi-optimale ailleurs. Cet ensemble peut être choisi par le statisticien et la vitesse suroptimale est atteinte pour l'erreur quadratique intégrée et la convergence uniforme presque sûre. Une version adaptative de l'estimateur est également considérée. Pour citer cet article : D. Bosq, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 591-595.

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We study a data-driven version of the density projection estimator in a general framework. We show that this estimator reaches a superoptimal rake on a dense set in the density class, and a quasi-optimal rake elsewhere. This set can be chosen by the statistician, and the superoptimal speed is reached for integrated quadratic error and almost sure uniform convergence. An adaptive version of the estimator is also considered. To cite this article: D. Bosq, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 591-595.

The full text of this article is available in PDF format.

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