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December, 1992 Variable Bandwidth and Local Linear Regression Smoothers
Jianqing Fan, Irene Gijbels
Ann. Statist. 20(4): 2008-2036 (December, 1992). DOI: 10.1214/aos/1176348900


In this paper we introduce an appealing nonparametric method for estimating the mean regression function. The proposed method combines the ideas of local linear smoothers and variable bandwidth. Hence, it also inherits the advantages of both approaches. We give expressions for the conditional MSE and MISE of the estimator. Minimization of the MISE leads to an explicit formula for an optimal choice of the variable bandwidth. Moreover, the merits of considering a variable bandwidth are discussed. In addition, we show that the estimator does not have boundary effects, and hence does not require modifications at the boundary. The performance of a corresponding plug-in estimator is investigated. Simulations illustrate the proposed estimation method.


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Jianqing Fan. Irene Gijbels. "Variable Bandwidth and Local Linear Regression Smoothers." Ann. Statist. 20 (4) 2008 - 2036, December, 1992.


Published: December, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0765.62040
MathSciNet: MR1193323
Digital Object Identifier: 10.1214/aos/1176348900

Primary: 62G07
Secondary: 62G20, 62J99

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 4 • December, 1992
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