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.
We consider the problem of the local linear estimation of the regression operator when the regressor is functional. We construct an estimator by the kNN 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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Mohammed Attouch 1 ; Ali Laksaci 1 ; Fatima Rafaa 1
@article{CRMATH_2017__355_7_824_0, author = {Mohammed Attouch and Ali Laksaci and Fatima Rafaa}, title = {Estimation locale lin\'eaire de la r\'egression non param\'etrique fonctionnelle par la m\'ethode des \protect\emph{k} plus proches voisins}, journal = {Comptes Rendus. Math\'ematique}, pages = {824--829}, publisher = {Elsevier}, volume = {355}, number = {7}, year = {2017}, doi = {10.1016/j.crma.2017.05.007}, language = {fr}, }
TY - JOUR AU - Mohammed Attouch AU - Ali Laksaci AU - Fatima Rafaa TI - Estimation locale linéaire de la régression non paramétrique fonctionnelle par la méthode des k plus proches voisins JO - Comptes Rendus. Mathématique PY - 2017 SP - 824 EP - 829 VL - 355 IS - 7 PB - Elsevier DO - 10.1016/j.crma.2017.05.007 LA - fr ID - CRMATH_2017__355_7_824_0 ER -
%0 Journal Article %A Mohammed Attouch %A Ali Laksaci %A Fatima Rafaa %T Estimation locale linéaire de la régression non paramétrique fonctionnelle par la méthode des k plus proches voisins %J Comptes Rendus. Mathématique %D 2017 %P 824-829 %V 355 %N 7 %I Elsevier %R 10.1016/j.crma.2017.05.007 %G fr %F CRMATH_2017__355_7_824_0
Mohammed Attouch; Ali Laksaci; Fatima Rafaa. Estimation locale linéaire de la régression non paramétrique fonctionnelle par la méthode des k plus proches voisins. Comptes Rendus. Mathématique, Volume 355 (2017) no. 7, pp. 824-829. doi : 10.1016/j.crma.2017.05.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.05.007/
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