Title: Sufficient dimension reduction for high dimensional data

Abstract: The high dimensional data generated from modern scientific discoveries introduces unique challenges to statistical modeling. Sufficient dimension reduction (SDR) is a useful tool to bridge the gap through projection subspace recovery. In this study, a new formulation is proposed based on the Hellinger integral of order two, a natural measure of the regression information contained in a high dimensional predictor subspace. The response may be either continuous, discrete or multivariate. The link between local and global central subspaces is established. Relative to existing methods, its overall performance is broadly comparable. Computationally, it is very efficient, allowing larger problems to be tackled.