[Normalité asymptotique des composantes d'un modèle additif de régression dans le cas de processus en temps continu]
Dans l'estimation de la régression multivariée, la vitesse de convergence dépend de la dimension du régresseur. Ce phénomène, connu sous le nom de fléau de la dimension, a motivé plusieurs travaux. Le modèle additif, introduit par Stone [C.J. Stone, Additive regression and other nonparametric models, Ann. Statist. 13 (2) (1985) 689–705. [9]], propose une réponse à ce problème. Dans le cadre des processus à temps continu, nous utilisons la méthode d'intégration marginale pour obtenir la vitesse de convergence quadratique et la normalité asymptotique des composantes additives.
In multivariate regression estimation, the rate of convergence depends on the dimension of the regressor. This fact, known as the curse of the dimensionality, motivated several works. The additive model, introduced by Stone [C.J. Stone, Additive regression and other nonparametric models, Ann. Statist. 13 (2) (1985) 689–705. [9]], offers an efficient response to this problem. In the setting of continuous time processes, using the marginal integration method, we obtain the quadratic convergence rate and the asymptotic normality of the components of the additive model.
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@article{CRMATH_2008__346_15-16_901_0,
author = {Debbarh, Mohammed and Maillot, Bertrand},
title = {Asymptotic normality of the additive regression components for continuous time processes},
journal = {Comptes Rendus. Math\'ematique},
pages = {901--906},
publisher = {Elsevier},
volume = {346},
number = {15-16},
year = {2008},
doi = {10.1016/j.crma.2008.06.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.06.012/}
}
TY - JOUR AU - Debbarh, Mohammed AU - Maillot, Bertrand TI - Asymptotic normality of the additive regression components for continuous time processes JO - Comptes Rendus. Mathématique PY - 2008 SP - 901 EP - 906 VL - 346 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.06.012/ DO - 10.1016/j.crma.2008.06.012 LA - en ID - CRMATH_2008__346_15-16_901_0 ER -
%0 Journal Article %A Debbarh, Mohammed %A Maillot, Bertrand %T Asymptotic normality of the additive regression components for continuous time processes %J Comptes Rendus. Mathématique %D 2008 %P 901-906 %V 346 %N 15-16 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.06.012/ %R 10.1016/j.crma.2008.06.012 %G en %F CRMATH_2008__346_15-16_901_0
Debbarh, Mohammed; Maillot, Bertrand. Asymptotic normality of the additive regression components for continuous time processes. Comptes Rendus. Mathématique, Tome 346 (2008) no. 15-16, pp. 901-906. doi : 10.1016/j.crma.2008.06.012. http://www.numdam.org/articles/10.1016/j.crma.2008.06.012/
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