Groupwise sufficient dimension reduction via conditional distance clustering

Abstract

It becomes increasingly common to incorporate the predictors’ grouping knowledge into dimension reduction techniques. In this article, we establish a complete framework named groupwise sufficient dimension reduction via conditional distance clustering, when the grouping information is unknown. We introduce a simple-type conditional dependence measurement and a corresponding conditional independence test. A clustering procedure based on the measurement and test is constructed to detect the suitable group structure. Finally we conduct sufficient dimension reduction under the obtained structure. Both simulations and a real data analysis demonstrate that the clustering strategy is effective, and the groupwise sufficient dimension reduction method is generally superior to the classical sufficient dimension reduction method.