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.
Reviewer: H.Dehling (Groningen)
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62E20 | Asymptotic distribution theory in statistics |
| 62G07 | Density estimation |
| 62G20 | Asymptotic properties of nonparametric inference |
Keywords:
time series; general weights; Gasser-Müller estimate; autoregressive processes; fixed design; strict stationarity; bounded case; unbounded case; kernel type smoothers; asymptotic normality; nonparametric regression models; dependent errors; stationary strongly mixing process; Priestley-Chao estimatorsReferences:
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