Statistics
Asymptotic normality of the additive regression components for continuous time processes
Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 901-906.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.06.012
Debbarh, Mohammed 1; Maillot, Bertrand 1

1 L.S.T.A., Université de Paris 6, 175, rue du Chevaleret, 75013 Paris, France
@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, Volume 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/

[1] Banon, G. Nonparametric identification for diffusion processes, SIAM J. Control Optim., Volume 16 (1978) no. 3, pp. 380-395

[2] Bosq, D. Nonparametric Statistics for Stochastic Processes, Estimation and Prediction, Lecture Notes in Statistics, vol. 110, Springer-Verlag, New York, 1998

[3] Bosq, D. Vitesses optimales et superoptimales des estimateurs fonctionnels pour les processus à temps continu, C. R. Acad. Sci. Paris Sér. I Math., Volume 317 (1993) no. 11, pp. 1075-1078

[4] Camlong-Viot, C.; Sarda, P.; Vieu, P. Additive time series: The kernel integration method, Math. Methods Statist., Volume 9 (2000) no. 4, pp. 358-375

[5] Cheze-Payaud, N. Nonparametric regression and prediction for continuous-time processes, Publ. Inst. Statist. Univ. Paris, Volume 38 (1994) no. 2, pp. 37-58

[6] Jones, M.C.; Davies, S.J.; Park, B.U. Versions of kernel-type regression estimators, J. Amer. Statist. Assoc., Volume 89 (1994) no. 427, pp. 825-832

[7] Linton, O.; Nielsen, J.P. A kernel method of estimating structured nonparametric regression based on marginal integration, Biometrika, Volume 82 (1995) no. 1, pp. 93-100

[8] Newey, W.K. Kernel estimation of partial means and a general variance estimator, Econometric Theory, Volume 10 (1994) no. 2, pp. 233-253

[9] Stone, C.J. Additive regression and other nonparametric models, Ann. Statist., Volume 13 (1985) no. 2, pp. 689-705

Cited by Sources: