Shrinkage Inverse Regression Estimation for Model Free Variable Selection

Summary. The family of inverse regression estimators recently proposed by Cook and Ni (2005) have proven effective in dimension reduction by transforming the high-dimensional predictor vector to its low-dimensional projections. In this article, we propose a general shrinkage estimation strategy for the entire inverse regression es-timation family that is capable of simultaneous dimension reduction and variable selection. We demonstrate that the new estimators achieve consistency in variable selection without requiring any traditional model, meanwhile retaining the root-n es-timation consistency of the dimension reduction basis. We also show the effectiveness of the new estimators through both simulation and real data analysis