A model-free variable selection method for reducing the number of redundant variables

Under the sufficient dimension reduction (SDR) framework, we propose a model-free variable selection method for reducing the number of redundant predictors. The method adopts the distance correlation as a dependence measure to quantify the relevance and redundancy of a predictor, and searches for a set of the relevant but non-redundant predictors. Two forward screening algorithms are given to find an approximate solution to the set of the relevant but non-redundant predictors. The screening consistency of the proposed method and algorithms has been fully studied. The effectiveness of the proposed method and algorithms is illustrated by the simulation experiments and two real examples. The experimental results show that the proposed method can effectively exclude the redundant predictors and yield a more parsimonious subset of the relevant predictors.