Sufficient Dimension Reduction in Causal Inference

Abstract

Investigating the causal effect of a treatment on an outcome is often the primary interest in medical and social studies. While the estimation of average treatment effects usually involves multivariate confounders, dimension reduction is often desirable and sometimes inevitable. In this talk, I will consider the Neyman-Rubin model and clarify the definition of a central subspace that is relevant for the efficient estimation of average treatment effects. In practice, a cross-validation type estimation criterion is proposed to simultaneously estimate the structural dimensions, the basis matrices of the proposed central subspaces, and the optimal bandwidths for estimating the conditional treatment effects. Semiparametric efficient estimation of average treatment effects can be achieved by averaging the conditional treatment effects with a different data-adaptive bandwidth to ensure optimal under-smoothing. This approach is also extended to the case when the treatment variable is continuous or when some confounders are not available.