Smoothing parameter selection in nonparametric regression using an improved kullback information criterion

Abstract

Many different methods for constructing nonparametric estimates of a smooth regression function use a smoothing parameter to control the amount of smoothing performed on a given data set. In this paper, a method based on an improved version of Kullback Information Criterion (KIC), termed KICc1 is derived and implemented for selecting the appropriate smoothing parameter for any type of linear smoother. Monte Carlo simulations demonstrate that KICc1 , unlike the Generalized Cross Validation (GCV) method, has less tendency to undersmooth and exhibits low variability specially for low SNR. Also, it is very competitive with the plug-in method and performs well when this last fails. Furthermore, KICc1 slightly outperforms its analogue AICc1 based on the known Akaike Information criterion (AIC).