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Asymptotically efficient estimates for nonparametric regression models. (English) Zbl 1089.62044

Summary: The paper deals with estimation problems of regression functions at a given state point in nonparametric regression models with Gaussian noises and with non-Gaussian noises having unknown distribution. An asymptotically efficient kernel estimator is constructed for a minimax risk.

MSC:

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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