Iterative application of dimension reduction methods

Abstract

The goal of this article is to introduce an iterative application of dimension reduction methods. It is known that in some situations, methods such as Sliced Inverse Regression (SIR), Ordinary Least Squares (OLS) and Cumulative Mean Estimation (CUME) are able to find only a partial basis for the dimension reduction subspace. However, for many models these methods are very good estimators of this partial basis. In this paper we propose a simple iterative procedure which differs from existing combined approaches in the sense that the initial partial basis is estimated first and the second dimension reduction approach seeks only the remainder of the dimension reduction subspace. Our approach is compared against that of existing combined dimension reduction approaches via simulated data as well as two example data sets.