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Comptes Rendus Mathématique
Volume 345, n° 9
pages 519-522 (novembre 2007)
Doi : 10.1016/j.crma.2007.10.015
Received : 15 Mars 2007 ;  accepted : 2 October 2007
Régression fonctionnelle sur composantes principales pour variable explicative bruitée
Functional principal component regression with noisy covariate
 

Christophe Crambes
Laboratoire de statistique et probabilités, Université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse cedex, France 

Résumé

Cette Note a pour objet une étude du modèle linéaire fonctionnel lorsque la variable explicative est bruitée. Pour chaque courbe explicative bruitée, on utilise une méthode de lissage à noyau, puis on effectue une régression fonctionnelle sur composantes principales. On présente la procédure dʼestimation du coefficient fonctionnel du modèle, ainsi quʼun résultat de convergence de lʼestimateur construit. Pour citer cet article : C. Crambes, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

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

This Note deals with a study of the functional linear model when the covariate is noisy. We smooth each noisy curve using a kernel smoothing method, and then a functional principal component regression is done. We present the estimation procedure of the functional coefficient of the model, as well as a convergence result of the estimator. To cite this article: C. Crambes, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

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


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