Dong, Yuexiao2020-10-272020-10-272016965642564http://hdl.handle.net/20.500.12613/1932In 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.118 pagesengIN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available.http://rightsstatements.org/vocab/InC/1.0/StatisticsText