An Effective Bandwidth Selector for Local Least Squares Regression
An Effective Bandwidth Selector for Local Least Squares Regression
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DOI：
10.1080/01621459.1995.10476630
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发表时间：
1995-12
影响因子：
3.7
通讯作者：
D. Ruppert;S. Sheather;M. Wand
中科院分区：
文献类型：
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作者：
D. Ruppert;S. Sheather;M. Wand
摘要局部最小二乘核回归为非参数回归或“散点图平滑”问题提供了一个有吸引力的解决方案，例如，Fan所证明的。任何散点图平滑器的实际实施大大提高了一个可靠的规则自动选择的平滑参数的可用性。在这篇文章中，我们应用插件的带宽选择的思想来开发本地线性平方核估计的平滑参数的选择策略。我们的结果适用于奇次局部多项式拟合，并可以扩展到其他设置，如导数估计和多元非参数回归。一个重要的情况下，与单变量预测的局部线性拟合的实施在实践中表现良好。我们的工作的一个副产品是一类非参数方差估计的发展，基于本地最小二乘的想法，和插件的规则，他们的实施。
Abstract Local least squares kernel regression provides an appealing solution to the nonparametric regression, or “scatterplot smoothing,” problem, as demonstrated by Fan, for example. The practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter. In this article we apply the ideas of plug-in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators. Our results are applicable to odd-degree local polynomial fits and can be extended to other settings, such as derivative estimation and multiple nonparametric regression. An implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice. A by-product of our work is the development of a class of nonparametric variance estimators, based on local least squares ideas, and plug-in rules for their implementation.