Dimension reduction based linear surrogate variable approach for model free variable selection

Most of variable selection methods depend on the model assumptions, while sufficient dimension reduction is a nonparametric method to deal with high dimensional data. In this paper we aim at integrating sufficient dimension reduction into variable selection. A two stage procedure is proposed. First, we obtain dimension reduction directions and integrate them to construct a variable which is linearly dependent on predictors. Then by treating this constructed variable as a new response, we use the traditional variable selection methods such as adaptive LASSO to conduct variable selection. We call such a procedure as dimension reduction based linear surrogate variable (LSV) method. To illustrate that it has wide application, we also apply it to variable selection for the problem of missing responses. Extensive simulation studies show that it is more robust than the variable selection methods depending on model assumptions, and more efficient than the other model-free variable selection methods. Another advantage of the LSV is that it can be easily implemented. A real example is given to illustrate the proposed method.