Transformed sufficient dimension reduction

We propose a general framework for dimension reduction in regression to fill the gap between linear and fully nonlinear dimension reduction. Themain idea is to first transformeach of the raw predictors monotonically and then search for a low-dimensional projection in the space defined by the transformed variables. Both user-specified and data-driven transformations are suggested. In each case, the methodology is first discussed in generality and then a representative method is proposed and evaluated by simulation. The proposed methods are applied to a real dataset.