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Comptes Rendus Mathématique
Volume 355, n° 7
pages 824-829 (juillet 2017)
Doi : 10.1016/j.crma.2017.05.007
Received : 3 February 2017 ;  accepted : 24 May 2017
Estimation locale linéaire de la régression non paramétrique fonctionnelle par la méthode des k plus proches voisins
Local linear estimate of the regression operator by the k NN method
 

Mohammed Attouch , Ali Laksaci , Fatima Rafaa
 Laboratoire de Statistique et Processus Stochastiques, Université Djillali Liabes, Sidi Bel Abbes, Algérie 

Résumé

Nous étudions l'estimation locale linéaire de l'opérateur de régression lorsque la variable explicative prend ses valeurs dans un espace semi-métrique. Nous construisons un estimateur par la méthode des k plus proches voisins. Deux propriétés asymptotiques de cet estimateur seront établies. Dans la première partie, nous prouvons la convergence presque complète ponctuelle, tandis que, dans la deuxième, nous montrons la convergence presque complète uniforme sur le nombre de voisins.

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Abstract

We consider the problem of the local linear estimation of the regression operator when the regressor is functional. We construct an estimator by the k NN method and we study its asymptotic properties. Precisely, we establish the almost complete consistency of this estimator with rate both pointwise and uniform on the number of neighbor cases.

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