Adaptive Spline Smoothing in Non-Gaussian Regression Models

A convenient and efficient algorithm for penalized likelihood smoothing spline regression is proposed and illustrated. The amount of smoothing is tuned adaptively via the generalized cross-validation method. Under certain conditions, the method is shown to approximately minimize the expected Kullback-Leibler discrepancy in modeling one-parameter exponential family observations through the canonical parameter. The algorithm is applied to fit logistic models using interaction splines. This research extends the recent algorithmic development of computing smoothing splines, provides further justification for the heuristics of O'Sullivan, Yandell, and Raynor (1986) on the property of generalized cross-validation in this setting, and experiments with interaction splines.