Modern graphical tools have enhanced our ability to learn many things from data directly. In recent years, dimension reduction has proven to be an effective tool for generating lo dimensional summary plots without appreciable loss of information. Some well-known inverse regression methods for dimension reduction such as SIR (Li, 1991) and SAVE (Cook & Weisberg, 1991) have been developed to estimate summary plots for regression and discriminant analysis. In this article, we suggest a new method (SAT) that makes use of inverse third moments. This method can find structure beyond that found by SIR and SAVE, particularly regression mixtures. Examples illustrating the theory are presented.
Estimating Central Subspaces Via Inverse Third Moments