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Local linear kernel estimation for discontinuous nonparametric regression functions. (English) Zbl 0953.62038

The authors consider the nonparametric regression model with fixed design and assume that the regression function has a change-point. They apply the method of local linear kernel smoothing to construct estimates for the location of the jump point and the size of the jump. Based on results on the asymptotic behavior of these estimates the asymptotic normality of the integrated squared error (ISE) of the corresponding regression estimate is derived. Moreover, it is shown that the rate of convergence of the ISE of the local linear estimator is better than that of the Nadaraya-Watson and the Gasser–Müller estimators.
Reviewer: H.Liero (Potsdam)

MSC:

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

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