Open Access
April 2007 Reducing variance in univariate smoothing
Ming-Yen Cheng, Liang Peng, Jyh-Shyang Wu
Ann. Statist. 35(2): 522-542 (April 2007). DOI: 10.1214/009053606000001398


A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged. The nearby points are chosen to maximize the variance reduction. We study in detail the case of univariate local linear regression. While the new estimator retains many advantages of the local linear estimator, it has appealing asymptotic relative efficiencies. Bandwidth selection rules are available by a simple constant factor adjustment of those for local linear estimation. A simulation study indicates that the finite sample relative efficiency often matches the asymptotic relative efficiency for moderate sample sizes. This technique is very general and has a wide range of applications.


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Ming-Yen Cheng. Liang Peng. Jyh-Shyang Wu. "Reducing variance in univariate smoothing." Ann. Statist. 35 (2) 522 - 542, April 2007.


Published: April 2007
First available in Project Euclid: 5 July 2007

zbMATH: 1117.62038
MathSciNet: MR2336858
Digital Object Identifier: 10.1214/009053606000001398

Primary: 62G05 , 62G08
Secondary: 60G20

Keywords: bandwidth , coverage probability , ‎kernel‎ , local linear regression , nonparametric smoothing , variance reduction

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 2 • April 2007
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