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Estimating linear functionals of the error distribution in nonparametric regression. (English) Zbl 1031.62033
Summary: This paper addresses estimation of linear functionals of the error distribution in nonparametric regression models. It derives an i.i.d. representation for the empirical estimator based on residuals, using undersmoothed estimators for the regression curve. Asymptotic efficiency of the estimator is proved. Estimation of the error variance is discussed in detail. In this case, undersmoothing is not necessary.

MSC:
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
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