Sufficient dimension reduction through discretization-expectation estimation

In the context of sufficient dimension reduction, the goal is to parsimoniously recover the central subspace of a regression model. Many inverse regression methods use slicing estimation to recover the central subspace. The efficacy of slicing estimation depends heavily upon the number of slices. However, the selection of the number of slices is an open and long-standing problem. In this paper, we propose a discretization-expectation estimation method, which avoids selecting the number of slices, while preserving the integrity of the central subspace. This generic method assures root-n consistency and asymptotic normality of slicing estimators for many inverse regression methods, and can be applied to regressions with multivariate responses. A BIC-type criterion for the dimension of the central subspace is proposed. Comprehensive simulations and an illustrative application show that our method compares favourably with existing estimators.