Optimal transformation: A new approach for covering the central subspace

This paper studies a general family of methods for sufficient dimension reduction (SDR) called the test function (TF), based on the introduction of a nonlinear transformation of the response. By considering order 1 and 2 conditional moments of the predictors given the response, we distinguish two classes of methods. The optimal members of each class are calculated with respect to the asymptotic mean squared error between the central subspace (CS) and its estimate. Moreover the theoretical background of TF is developed under weaker conditions than the existing methods. Accordingly, simulations confirm that the resulting methods are highly accurate.