VARIABLE BANDWIDTH AND LOCAL LINEAR-REGRESSION SMOOTHERS
VARIABLE BANDWIDTH AND LOCAL LINEAR-REGRESSION SMOOTHERS
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DOI：
10.1214/aos/1176348900
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发表时间：
1992-12-01
影响因子：
4.5
通讯作者：
GIJBELS, I
中科院分区：
文献类型：
--
作者：
FAN, JQ;GIJBELS, I
本文介绍了一种估计均值回归函数的非参数方法。该方法结合了局部线性平滑和变带宽的思想。因此，它也继承了这两种方法的优点。给出了估计量的条件均方差和均方差的表达式。最小的MISE导致一个明确的公式为可变带宽的最佳选择。此外，还讨论了考虑可变带宽的优点。此外，我们证明了估计量没有边界效应，因此不需要在边界处修改。研究了相应的插件估计器的性能。仿真验证了所提出的估计方法。
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.