In this paper we demonstrate that a higher-ranking principal component of the predictor tends to have a stronger correlation with the response in single index models and sufficient dimension reduction. This tendency holds even though the orientation of the predictor is not designed in any way to...

In this paper we propose a dimension reduction method for estimating the directions in a multiple-index regression based on information extraction. This extends the recent work of Yin and Cook [X. Yin, R.D. Cook, Direction estimation in single-index regression, Biometrika 92 (2005) 371-384] who...