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Comptes Rendus Mathématique
Volume 346, n° 15-16
pages 901-906 (août 2008)
Doi : 10.1016/j.crma.2008.06.012
Received : 29 August 2007 ;  accepted : 27 June 2008
Asymptotic normality of the additive regression components for continuous time processes
Normalité asymptotique des composantes dʼun modèle additif de régression dans le cas de processus en temps continu
 

Mohammed Debbarh , Bertrand Maillot
L.S.T.A., Université de Paris 6, 175, rue du Chevaleret, 75013 Paris, France 

Abstract

In multivariate regression estimation, the rate of convergence depends on the dimension of the regressor. This fact, known as the curse of the dimensionality , motivated several works. The additive model, introduced by Stone [C.J. Stone, Additive regression and other nonparametric models, Ann. Statist. 13 (2) (1985) 689–705. [9]], offers an efficient response to this problem. In the setting of continuous time processes, using the marginal integration method, we obtain the quadratic convergence rate and the asymptotic normality of the components of the additive model. To cite this article: M. Debbarh, B. Maillot, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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

Dans lʼestimation de la régression multivariée, la vitesse de convergence dépend de la dimension du régresseur. Ce phénomène, connu sous le nom de fléau de la dimension , a motivé plusieurs travaux. Le modèle additif, introduit par Stone [C.J. Stone, Additive regression and other nonparametric models, Ann. Statist. 13 (2) (1985) 689–705. [9]], propose une réponse à ce problème. Dans le cadre des processus à temps continu, nous utilisons la méthode dʼintégration marginale pour obtenir la vitesse de convergence quadratique et la normalité asymptotique des composantes additives. Pour citer cet article : M. Debbarh, B. Maillot, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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


© 2008  Published by Elsevier Masson SAS de la part de Académie des sciences.
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