Estimation of projection pursuit regression via alternating linearization

Abstract

The projection pursuit regression (PPR) has played an important role in statistical modeling. It can be used both as a data model for statistical interpretation and as an algorithmic model for approximating general non-parametric regressions. Existing estimation methods of PPR usually involve complicated minimization in order to achieve desired efficiency under general settings. This paper presents an algorithm by alternatively linearizing the estimation loss function, referred to as aPPR hereafter, which is easy to implement. The asymptotic theory is also established for both the PPR data model and the algorithmic model. Numerical performance of aPPR in model estimation and model interpretation is demonstrated through simulations and real data analysis.