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Fixed design regression for time series: Asymptotic normality. (English) Zbl 0764.62073
The authors study nonparametric regression models with dependent errors. More specifically, it is assumed that the error variables form a stationary strongly mixing process. Kernel type smoothers are studied as estimators of the regression function, including as examples the Gasser- Müller and Priestley-Chao estimators. Asymptotic normality of these estimators is established under various assumptions on the mixing rates and on the weights.

MSC:
62M10Time series, auto-correlation, regression, etc. (statistics)
62E20Asymptotic distribution theory in statistics
62G07Density estimation
62G20Nonparametric asymptotic efficiency