Nous étudions l'estimateur à noyau de la régression quand la variable explicative prend ses valeurs dans un espace semi-métrique. Nous établissons sa consistance en moyenne d'ordre p et presque sûre et nous donnons des bornes supérieures de ces erreurs d'estimation sous des conditions générales. Nous appliquons ces résultats à la discrimination de variables d'un espace semi-métrique et les illustrons par l'exemple du processus de Wiener comme variable explicative.
We study a nonparametric regression estimator when the explanatory variable takes its values in a semi-metric space. We establish some asymptotic results and give upper bounds of the p-mean and the almost sure estimation errors under general conditions. We end by an application to the discrimination in a semi-metric space and illustrate the results by the example of Wiener process as an explanatory variable.
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@article{CRMATH_2003__336_1_75_0,
author = {Dabo-Niang, Sophie and Rhomari, Noureddine},
title = {Estimation non param\'etrique de la r\'egression avec variable explicative dans un espace m\'etrique},
journal = {Comptes Rendus. Math\'ematique},
pages = {75--80},
publisher = {Elsevier},
volume = {336},
number = {1},
year = {2003},
doi = {10.1016/S1631-073X(02)00012-2},
language = {fr},
url = {https://www.numdam.org/articles/10.1016/S1631-073X(02)00012-2/}
}
TY - JOUR AU - Dabo-Niang, Sophie AU - Rhomari, Noureddine TI - Estimation non paramétrique de la régression avec variable explicative dans un espace métrique JO - Comptes Rendus. Mathématique PY - 2003 SP - 75 EP - 80 VL - 336 IS - 1 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/S1631-073X(02)00012-2/ DO - 10.1016/S1631-073X(02)00012-2 LA - fr ID - CRMATH_2003__336_1_75_0 ER -
%0 Journal Article %A Dabo-Niang, Sophie %A Rhomari, Noureddine %T Estimation non paramétrique de la régression avec variable explicative dans un espace métrique %J Comptes Rendus. Mathématique %D 2003 %P 75-80 %V 336 %N 1 %I Elsevier %U https://www.numdam.org/articles/10.1016/S1631-073X(02)00012-2/ %R 10.1016/S1631-073X(02)00012-2 %G fr %F CRMATH_2003__336_1_75_0
Dabo-Niang, Sophie; Rhomari, Noureddine. Estimation non paramétrique de la régression avec variable explicative dans un espace métrique. Comptes Rendus. Mathématique, Tome 336 (2003) no. 1, pp. 75-80. doi : 10.1016/S1631-073X(02)00012-2. https://www.numdam.org/articles/10.1016/S1631-073X(02)00012-2/
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