zbMATH — the first resource for mathematics

Asymptotic normality of the additive regression components for continuous time processes. (English. Abridged French version) Zbl 1144.62076
Summary: 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 C. J. Stone [Additive regression and other nonparametric models. Ann. Stat. 13, 689–705 (1985; Zbl 0605.62065)], 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.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G08 Nonparametric regression and quantile regression
62E20 Asymptotic distribution theory in statistics
Full Text: DOI arXiv
[1] Banon, G., Nonparametric identification for diffusion processes, SIAM J. control optim., 16, 3, 380-395, (1978) · Zbl 0404.93045
[2] Bosq, D., Nonparametric statistics for stochastic processes, estimation and prediction, Lecture notes in statistics, vol. 110, (1998), Springer-Verlag New York · Zbl 0902.62099
[3] Bosq, D., Vitesses optimales et superoptimales des estimateurs fonctionnels pour LES processus à temps continu, C. R. acad. sci. Paris Sér. I math., 317, 11, 1075-1078, (1993) · Zbl 0791.60027
[4] Camlong-Viot, C.; Sarda, P.; Vieu, P., Additive time series: the kernel integration method, Math. methods statist., 9, 4, 358-375, (2000) · Zbl 1008.62039
[5] Cheze-Payaud, N., Nonparametric regression and prediction for continuous-time processes, Publ. inst. statist. univ. Paris, 38, 2, 37-58, (1994) · Zbl 0794.62027
[6] Jones, M.C.; Davies, S.J.; Park, B.U., Versions of kernel-type regression estimators, J. amer. statist. assoc., 89, 427, 825-832, (1994) · Zbl 0804.62043
[7] Linton, O.; Nielsen, J.P., A kernel method of estimating structured nonparametric regression based on marginal integration, Biometrika, 82, 1, 93-100, (1995) · Zbl 0823.62036
[8] Newey, W.K., Kernel estimation of partial means and a general variance estimator, Econometric theory, 10, 2, 233-253, (1994)
[9] Stone, C.J., Additive regression and other nonparametric models, Ann. statist., 13, 2, 689-705, (1985) · Zbl 0605.62065
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.