Slicing Inverse Regression

Abstract

Sliced inverse regression (SIR) is a computationally simple and fast method for reducing the dimension of the explanatory variables x in regression problems. SIR does the following: (a) it determines the dimension of a subspace spanned by the linear combinations of x that contains all information needed for describing the relationship between x and the output variable Y ; (b) it assesses the significance of the contribution from each input variable to dimension reduction; (c) it provides a foundation for further exploratory graphical analysis and nonparametric regression. (Color versions of the figures presented in this article can be obtained from http://gap.stat.sinica.edu.tw )