Robust inverse regression for dimension reduction

Classical sufficient dimension reduction methods are sensitive to outliers present in predictors, and may not perform well when the distribution of the predictors is heavy-tailed. In this paper, we propose two robust inverse regression methods which are insensitive to data contamination: weighted inverse regression estimation and sliced inverse median estimation. Both weighted inverse regression estimation and sliced inverse median estimation produce unbiased estimates of the central space when the predictors follow an elliptically contoured distribution. Our proposals are compared with existing robust dimension reduction procedures through comprehensive simulation studies and an application to the New Zealand mussel data. It is demonstrated that our methods have better overall performances than existing robust procedures in the presence of potential outliers and/or inliers.