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An Effective Bandwidth Selector for Local Least Squares Regression

D. Ruppert, S. J. Sheather and M. P. Wand
Journal of the American Statistical Association
Vol. 90, No. 432 (Dec., 1995), pp. 1257-1270
DOI: 10.2307/2291516
Stable URL: http://www.jstor.org/stable/2291516
Page Count: 14
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An Effective Bandwidth Selector for Local Least Squares Regression
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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.

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