Sliced Regression for Dimension Reduction

By slicing the region of the response (Li, 1991, SIR) and applying local kernel regression (Xia et al., 2002, MAVE) to each slice, a new dimension reduction method is proposed. Compared with the traditional inverse regression methods, e.g. sliced inverse regression (Li, 1991), the new method is free of the linearity condition (Li, 1991) and enjoys much improved estimation accuracy. Compared with the direct estimation methods (e.g., MAVE), the new method is much more robust against extreme values and can capture the entire central subspace (Cook, 1998b, CS) exhaustively. To determine the CS dimension, a consistent crossvalidation (CV) criterion is developed. Extensive numerical studies including one real example confirm our theoretical findings