VARIABLE BANDWIDTH AND LOCAL LINEAR-REGRESSION SMOOTHERS

• 成果类型: Article
• 署名作者: FAN, JQ; GIJBELS, I
• 署名单位: Hasselt University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348900
• 发表日期: 1992
• 页码: 2008-2036
• 关键词: Nonparametric regression; kernel; estimators

摘要

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.