Multiple regression for single index model

Abstract

A simple method based on SIR (Sliced Inverse Regression) is proposed to explore an EDR vector for the single index model. We avoid the principle component analysis step of the original SIR by using two sample mean vectors in two slices of the response variable and their difference vector. The methodology can be effectively applied even when the number of covariates is large since it requires no matrix operation or iterative calculation.