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 [3] 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.