A new sufficient dimension reduction method via rank divergence

Sufficient dimension reduction is commonly performed to achieve data reduction and help data visualization. Its main goal is to identify functions of the predictors that are smaller in number than the predictors and contain the same information as the predictors for the response. In this paper, we are concerned with the linear functions of the predictors, which determine a central subspace that preserves sufficient information about the conditional distribution of a response given covariates. Many methods have been developed in the literature for the estimation of the central subspace. However, most of the existing sufficient dimension reduction methods are sensitive to outliers and require some strict restrictions on both covariates and response. To address this, we propose a novel dependence measure, rank divergence, and develop a rank divergence-based sufficient dimension reduction approach. The new method only requires some mild conditions on the covariates and response and is robust to outliers or heavy-tailed distributions. Moreover, it applies to both discrete or categorical covariates and multivariate responses. The consistency of the resulting estimator of the central subspace is established, and numerical studies suggest that it works well in practical situations.