A fast method for implementing Generalized Cross-Validation in multi-dimensional nonparametric regression

This article presents a modified Newton method for minimizing the Generalized Cross-Validation criterion, a commonly used smoothing parameter selection method in nonparametric regression. The method is applicable to higher dimensional problems such as additive and generalized additive models, and provides a computationally efficient alternative to full grid search in such cases. The implementation of the proposed method requires the estimation of a number of auxiliary quantities, and simple estimators are suggested. This article describes the methodology for local polynomial regression smoothing.