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.