[Asymptotic normality for the wavelets estimator of the additive regression components]
In the setting of the additive regression model, we show asymptotic normality of an wavelets estimators of the additive components pertaining with the marginal integration estimation method. Our proof use the usual ‘small blocks-big blocks’ and the central limit theorem for dependent random variables.
Dans le cadre des modèles additifs de régression, nous établissons la normalité asymptotique des estimateurs des composantes additives obtenues par la méthode d'intégration marginale d'un estimateur par ondelettes. Pour établir nos résultats nous utilisons la décomposition « grands blocs-petits blocs » et le théorème central limite pour des variables dépendantes.
Accepted:
Published online:
Mohammed Debbarh 1
@article{CRMATH_2006__343_9_601_0, author = {Mohammed Debbarh}, title = {Normalit\'e asymptotique de l'estimateur par ondelettes des composantes d'un mod\`ele additif de r\'egression}, journal = {Comptes Rendus. Math\'ematique}, pages = {601--606}, publisher = {Elsevier}, volume = {343}, number = {9}, year = {2006}, doi = {10.1016/j.crma.2006.10.003}, language = {fr}, }
TY - JOUR AU - Mohammed Debbarh TI - Normalité asymptotique de l'estimateur par ondelettes des composantes d'un modèle additif de régression JO - Comptes Rendus. Mathématique PY - 2006 SP - 601 EP - 606 VL - 343 IS - 9 PB - Elsevier DO - 10.1016/j.crma.2006.10.003 LA - fr ID - CRMATH_2006__343_9_601_0 ER -
Mohammed Debbarh. Normalité asymptotique de l'estimateur par ondelettes des composantes d'un modèle additif de régression. Comptes Rendus. Mathématique, Volume 343 (2006) no. 9, pp. 601-606. doi : 10.1016/j.crma.2006.10.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.10.003/
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