Reducing variance in univariate smoothing

• 成果类型: Article
• 署名作者: Cheng, Ming-Yen; Peng, Liang; Wu, Jyh-Shyang
• 署名单位: National Taiwan University; University System of Georgia; Georgia Institute of Technology; Tamkang University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001398
• 发表日期: 2007
• 页码: 522-542
• 关键词: local linear-regression; Nonparametric Regression; DENSITY-ESTIMATION; bias reduction; bandwidth; estimators

摘要

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.