Adaptive Bandwidth Choice for Kernel Regression

摘要

A data-based procedure is introduced for local bandwidth selection for kernelestimation of a regression function at a point. The estimated bandwidth is shown to be consistent and asymptotically normal as an estimator of the (asymptotic) optimal value for minimum mean square estimation. The rate of convergence is identical to that of plug-in bandwidth estimators. The proposed method has the practical advantage that it reduces the need for a priori values and does not require pilot estimates of the regression function, optimization of estimated objective functions or resampling. A small Monte Carlo study is used to examine the behavior of the new bandwidth estimator in a variety of situations. The resulting finite-sample mean square errors of the corresponding curve estimates are generally found to be less than or equal to those of an idealized plug-in estimator. Keywords: Curve estimation, Nonparametric regression, Smoothing. (kr)