Sparse sufficient dimension reduction

Existing sufficient dimension reduction methods suffer fromthe fact that each dimension reduction component is a linearcombination of all the original predictors, so that it is difficultto interpret the resulting estimates. We propose a unified estimationstrategy, which combines a regression-type formulation of sufficientdimension reduction methods and shrinkage estimation, to producesparse and accurate solutions. The method can be applied tomost existing sufficient dimension reduction methods such assliced inverse regression, sliced average variance estimationand principal Hessian directions. We demonstrate the effectivenessof the proposed method by both simulations and real data analysis.