Model-Free Variable Selection through Sufficient Dimension Reduction

Abstract

In this thesis we draw upon the natural connection between the fields of sufficient dimension reduction and variable selection to develop new theory and methods for model-free variable selection. After developing the natural connection between sufficient dimension reduction and model-free variable selection we introduce two approaches to select independent variables important to predicting the response variable without making any assumptions about the function form of the relationship between predictor and response. The first is a stepwise procedure and the second takes a penalized approach. Both are rooted in ordinary least squares regression but with modifications to facilitate model-free variable selection. We also introduce a set of transformations for model-free variable selection. Finally we develop a stepwise procedure that is able to select interaction terms in the model-free setting. We show the effectiveness of these methods through simulation studies and an analysis of real data.