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Additive regression model for stationary and ergodic continuous time processes. (English) Zbl 1380.62165
Summary: The main purpose of the present work is to introduce and investigate a simple kernel procedure based on marginal integration that estimates the regression function for stationary and ergodic continuous time processes in the setting of the additive model introduced by C. J. Stone [Ann. Stat. 13, 689–705 (1985; Zbl 0605.62065)]. We obtain the uniform almost sure consistency with exact rate and the asymptotic normality of the kernel-type estimators of the components of the additive model. Asymptotic properties of these estimators are obtained, under mild conditions, by means of martingale approaches. Finally, a general notion of the bootstrapped additive components, constructed by exchangeably weighting sample, is presented.

MSC:
62G08 Nonparametric regression and quantile regression
60G09 Exchangeability for stochastic processes
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
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