Summary: ELSEVIER Computational Statistics & Data Analysis 21 (1996) 501-531
Moderate projection pursuit
regression for multivariate
Norwegian ComputingCenter,P.O. Box 114 Blindern, N-0134, Oslo,Norway
Received August 1994;revised May 1995
Consider a regression problem with a multivariate response that we expect depends on a set of
predictor variables in a non-linear way. A method designed for such problems is projection pursuit
regression (PPR). PPR allows for very flexible modelling of the relationship between the response and
the predictor variables, but it can have severe problems due to overfitting when there are few or noisy
data. In this paper, I present a modified version of PPR called moderate PPR which is close to linear
reduced rank regression. Substantial numerical evidence is presented to show that moderate PPR
outperforms the ordinary PPR when the non-linearity is moderate and the data are few or noisy.
Further, moderate PPR is robust in the sense that it rarely performs much worse than the linear
reduced rank regression.