An autocorrelation criterion for bandwidth selection in nonparametric regression
In this note, we propose a new method for selecting the bandwidth parameter in nonparametric regression. While standard criteria, such as cross-validation, are based on the true regression curve about which we know little, we propose a criterion which focuses on the true errors about which assumptions may be made. Our proposal is to choose the bandwidth for which the residuals are as uncorrelated as possible. We use the Box-Pierce statistic as the objective to be minimized. In doing so, the behaviour of our residuals will be close to that of the true errors under the hypothesis of independent errors. A simulation study shows that our method succeeds in capturing the main features of the regression curve, in the sense that the number of turning-points of the curve is correctly estimated most of the time.
autocorrelation bandwidth selection nonparametric regression kernel methods goodness-of-fit statistic