General directional regression

Directional regression is an effective sufficient dimension reduction method which implicitly synthesizes the first two conditional moments. In this paper, we extend directional regression to a general family of estimators via the notion of general empirical directions. Data-driven method is used to identify the optimal estimator within this family. Based on the proposed general directional regression estimators, we develop a new methodology for nonlinear dimension reduction. Improvement of general directional regression over classical directional regression is demonstrated via simulation studies and an empirical study with the wine recognition data.