AN EFFECTIVE BANDWIDTH SELECTOR FOR LOCAL LEAST-SQUARES REGRESSION

Local least squares kernel regression provides an appealing solution t o 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 t his article we apply the ideas of plug-in bandwidth selection to devel op strategies for choosing the smoothing parameter of local linear squ ares kernel estimators. Our results are applicable to odd-degree local polynomial fits and can be extended to other settings, such as deriva tive estimation and multiple nonparametric regression. An implementati on in the important case of local linear fits with univariate predicto rs is shown to perform well in practice. A by-product of our work is t he development of a class of nonparametric variance estimators, based on local least squares' ideas, and plug-in rules for their implementat ion.