On dual model-free variable selection with two groups of variables

In the presence of two groups of variables, existing model-free variable selection methods only reduce the dimensionality of the predictors. We extend the popular marginal coordinate hypotheses Cook (2004) in the sufficient dimension reduction literature and consider the dual marginal coordinate hypotheses, where the role of the predictor and the response is not important. Motivated by canonical correlation analysis (CCA), we propose a CCA-based test for the dual marginal coordinate hypotheses, and devise a joint backward selection algorithm for dual model-free variable selection. The performances of the proposed test and the variable selection procedure are evaluated through synthetic examples and a real data analysis.