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.
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.
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@article{CRMATH_2016__354_8_847_0,
author = {Demongeot, Jacques and Laksaci, Ali and Naceri, Amina and Rachdi, Mustapha},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.05.017/}
}
TY - JOUR AU - Demongeot, Jacques AU - Laksaci, Ali AU - Naceri, Amina AU - Rachdi, Mustapha 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2016.05.017/ DO - 10.1016/j.crma.2016.05.017 LA - fr ID - CRMATH_2016__354_8_847_0 ER -
%0 Journal Article %A Demongeot, Jacques %A Laksaci, Ali %A Naceri, Amina %A Rachdi, Mustapha %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 %U http://www.numdam.org/articles/10.1016/j.crma.2016.05.017/ %R 10.1016/j.crma.2016.05.017 %G fr %F CRMATH_2016__354_8_847_0
Demongeot, Jacques; Laksaci, Ali; Naceri, Amina; Rachdi, Mustapha. Estimation locale linéaire de la fonction de régression pour des variables hilbertiennes. Comptes Rendus. Mathématique, Tome 354 (2016) no. 8, pp. 847-850. doi : 10.1016/j.crma.2016.05.017. http://www.numdam.org/articles/10.1016/j.crma.2016.05.017/
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