On Projection Pursuit Regression

Abstract

We construct a tractable mathematical model for kernel-based projection pursuit regression approximation. The model permits computation of explicit formulae for bias and variance of estimators. It is shown that the bias of an orientation estimate dominates error about the mean--indeed, the latter is asymptotically negligible in comparison with bias. However, bias and error about the mean are of the same order in the case of projection pursuit curve estimates. Implications of our formulae for bias and variance are discussed.