Estimating Those Transformations That Produce the Best-fitting Additive Model: Smoothers Versus Universal Approximators

Abstract

When estimating a generalized additive model, a crucial decision that must be made is the choice of underlying technique that will be used to estimate those transformations that produce the best-fitting model. Data smoothers and universal approximators are two opposing techniques that seem to hold the most promise. ACE (alternating conditional expectations) was developed by Breiman and Friedman and utilizes a super-smoother to determine conditional expectation estimates. It was intended to be used as a tool to estimate the optimal transformations for multiple regression problems. Generalized additive neural networks on the other hand depend on the use of universal approximators to compute the nonlinear univariate transformations for the independent variables. These two approaches are compared and illustrated with a suitable example from the literature.