The Annals of Statistics

Variable Bandwidth and Local Linear Regression Smoothers

Jianqing Fan and Irene Gijbels

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Abstract

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.

Article information

Source
Ann. Statist., Volume 20, Number 4 (1992), 2008-2036.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348900

Digital Object Identifier
doi:10.1214/aos/1176348900

Mathematical Reviews number (MathSciNet)
MR1193323

Zentralblatt MATH identifier
0765.62040

JSTOR
links.jstor.org

Subjects
Primary: 62G07: Density estimation
Secondary: 62G20: Asymptotic properties 62J99: None of the above, but in this section

Keywords
Boundary effects local linear smoother mean squared error nonparametric regression optimalities variable bandwidth

Citation

Fan, Jianqing; Gijbels, Irene. Variable Bandwidth and Local Linear Regression Smoothers. Ann. Statist. 20 (1992), no. 4, 2008--2036. doi:10.1214/aos/1176348900. https://projecteuclid.org/euclid.aos/1176348900


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