Automatic Selection of Parameters in Spline Regression via Kullback-Leibler Information

Based on Kullback-Leibler information we propose a data-driven selector, called GAIC (c) , for choosing parameters of regression splines in nonparametric regression via a stepwise forward/backward knot placement and deletion strategy 1]. This criterion uniies the commonly used information criteria and includes the Akaike information criterion (AIC) 2] and the corrected Akaike information criterion (AICC) 3] as special cases. To show the performance of GAIC (c) for c = 1=2, 3=4, 7=8, and 15=16, we compare it with cross-validation (CV), the generalized cross-validation (GCV), AIC, and AICC by an extensive simulation. Applications to the selection of the penalty parameters of smoothing splines are also discussed. Our simulation results indicate that the information criteria work well and are superior to cross-validation-based criteria in most of the cases considered, particularly in small sample cases. Under certain mild conditions, GAIC (c) is shown to be asymptotically optimal in choosing the number of equispaced and random knots of regression splines.