[Local linear estimation of the regression function with Hilbertian variables]
In this paper, we introduce a new nonparametric estimation of the regression function when both the response and the explanatory variables are of the functional kind. First, we construct a local linear estimator of this regression operator, then we state its rate for the uniform almost complete convergence. This latter is expressed as a function of the small ball probability of the predictor and as a function of the entropy of the set on which the uniformity is obtained.
Dans cette Note, nous étudions l'estimation non paramétrique de la fonction de régression, lorsque la variable réponse et la covariable sont fonctionnelles. Nous construisons un estimateur local linéaire de l'opérateur de régression, et nous évaluons son erreur d'estimation. Ensuite, nous démontrons sa convergence presque complète et uniforme. La vitesse de convergence obtenue est exprimée en fonction de la probabilité des petites boules de la covariable et en fonction de la fonction d'entropie de l'ensemble sur lequel la convergence uniforme est obtenue.
Accepted:
Published online:
Jacques Demongeot 1; Ali Laksaci 2; Amina Naceri 2; Mustapha Rachdi 3
@article{CRMATH_2016__354_8_847_0,
author = {Jacques Demongeot and Ali Laksaci and Amina Naceri and Mustapha Rachdi},
title = {Estimation locale lin\'eaire de la fonction de r\'egression pour des variables hilbertiennes},
journal = {Comptes Rendus. Math\'ematique},
pages = {847--850},
publisher = {Elsevier},
volume = {354},
number = {8},
year = {2016},
doi = {10.1016/j.crma.2016.05.017},
language = {fr},
}
TY - JOUR AU - Jacques Demongeot AU - Ali Laksaci AU - Amina Naceri AU - Mustapha Rachdi TI - Estimation locale linéaire de la fonction de régression pour des variables hilbertiennes JO - Comptes Rendus. Mathématique PY - 2016 SP - 847 EP - 850 VL - 354 IS - 8 PB - Elsevier DO - 10.1016/j.crma.2016.05.017 LA - fr ID - CRMATH_2016__354_8_847_0 ER -
%0 Journal Article %A Jacques Demongeot %A Ali Laksaci %A Amina Naceri %A Mustapha Rachdi %T Estimation locale linéaire de la fonction de régression pour des variables hilbertiennes %J Comptes Rendus. Mathématique %D 2016 %P 847-850 %V 354 %N 8 %I Elsevier %R 10.1016/j.crma.2016.05.017 %G fr %F CRMATH_2016__354_8_847_0
Jacques Demongeot; Ali Laksaci; Amina Naceri; Mustapha Rachdi. Estimation locale linéaire de la fonction de régression pour des variables hilbertiennes. Comptes Rendus. Mathématique, Volume 354 (2016) no. 8, pp. 847-850. doi : 10.1016/j.crma.2016.05.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.05.017/
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