Open Access
August 2017 On the Choice of Difference Sequence in a Unified Framework for Variance Estimation in Nonparametric Regression
Wenlin Dai, Tiejun Tong, Lixing Zhu
Statist. Sci. 32(3): 455-468 (August 2017). DOI: 10.1214/17-STS613


Difference-based methods do not require estimating the mean function in nonparametric regression and are therefore popular in practice. In this paper, we propose a unified framework for variance estimation that combines the linear regression method with the higher-order difference estimators systematically. The unified framework has greatly enriched the existing literature on variance estimation that includes most existing estimators as special cases. More importantly, the unified framework has also provided a smart way to solve the challenging difference sequence selection problem that remains a long-standing controversial issue in nonparametric regression for several decades. Using both theory and simulations, we recommend to use the ordinary difference sequence in the unified framework, no matter if the sample size is small or if the signal-to-noise ratio is large. Finally, to cater for the demands of the application, we have developed a unified R package, named VarED, that integrates the existing difference-based estimators and the unified estimators in nonparametric regression and have made it freely available in the R statistical program


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Wenlin Dai. Tiejun Tong. Lixing Zhu. "On the Choice of Difference Sequence in a Unified Framework for Variance Estimation in Nonparametric Regression." Statist. Sci. 32 (3) 455 - 468, August 2017.


Published: August 2017
First available in Project Euclid: 1 September 2017

zbMATH: 06870255
MathSciNet: MR3696005
Digital Object Identifier: 10.1214/17-STS613

Keywords: Difference-based estimator , Nonparametric regression , optimal difference sequence , ordinary difference sequence , residual variance

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.32 • No. 3 • August 2017
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