Tests in projection pursuit regression

Abstract

Projection Pursuit regression (PPR) approximates a regression function f ( X ) by a finite sum of ridge functions ∑ l=1 L f l ( α l T X) . When the explanatory vector X is normally distributed, Johansen and Johnstone (1990) gave an one-term approximation formula to the significance level of a test of H 0 : f= constant. In this paper, we generalize the one-term approximation to a two-term approximation and to the case when X has an arbitrary distribution based on a general projection pursuit regression index that we propose. The first term of our approximation is same as Johansen and Johnstone’s one-term approximation when X is normally distributed. Some simulations and applications will be presented and choices of L will be discussed.