This project is aimed to develop a model free variable selection method under the framework of sufficient dimension reduction. With many advantages over more traditional subset selection methods in linear models, regularization has been introduced to model free framework. However, there are only a few results on the consistency of variable selection and the efficiency of the estimation of the dimension reduction subspace. This is partly due to the fact that regularization is often applied to eigenvectors of candidate matrices instead of individual predictors. The investigator proposes a penalized objective function with adaptive shrinkages to select variables without rigid parametric or semi-parametric model assumptions. The proposed new approach synthesizes the progresses in two fronts of statistical research: regularization method in linear models and sufficient dimension reduction in regression.
Selection of important factors can provide a better understanding and interpretation of underlying scientific process, obtain numerically efficient and consistent results, and improve accuracy of prediction whenever applicable. It has become the focus of current research in areas for which data sets with hundreds and thousands of variables are quite common. Examples include bioinformatics, data mining, classification, and pattern recognition. With limited knowledge of the underlying models, good model free methods for selecting important variables are in high demand. This project will investigate model free methods for the selection of key variables. The research findings are expected to yield substantial gains in the efficiency of data management, especially for high dimensional cases which have been the hallmark of contemporary social, economic, and scientific data analysis.
