  We propose a new method for dimension reduction in regression using the first
two inverse moments. We develop corresponding weighted chi-squared tests for
the dimension of the regression. The proposed method considers linear
combinations of Sliced Inverse Regression (SIR) and the method using a new
candidate matrix which is designed to recover the entire inverse second moment
subspace. The optimal combination may be selected based on the p-values derived
from the dimension tests. Theoretically, the proposed method, as well as Sliced
Average Variance Estimate (SAVE), are more capable of recovering the complete
central dimension reduction subspace than SIR and Principle Hessian Directions
(pHd). Therefore it can substitute for SIR, pHd, SAVE, or any linear
combination of them at a theoretical level. Simulation study indicates that the
proposed method may have consistently greater power than SIR, pHd, and SAVE.
