Xinyi Xu ,Jingxiao Zhang

【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.

【Keywords】

sufficient dimension reduction, group structure, conditional independence, conditional distance clustering