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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.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G08 Nonparametric regression and quantile regression
62E20 Asymptotic distribution theory in statistics
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