Joint sufficient dimension reduction and estimation of conditional and average treatment effects
提出一种同时估计结构维数、联合中心子空间基矩阵和最优带宽的方法，用于高效估计条件及平均处理效应，并通过营养研究实例将协变量从11维降至1维。
The estimation of treatment effects based on observational data usually involves multiple confounders, and dimension reduction is often desirable and sometimes inevitable. We first clarify the definition of a central subspace that is relevant for the efficient estimation of average treatment effects. A criterion is then proposed to simultaneously estimate the structural dimension, the basis matrix of the joint central subspace, and the optimal bandwidth for estimating the conditional treatment effects. The method can easily be implemented by forward selection. 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 undersmoothing. Asymptotic properties of the estimated joint central subspace and the corresponding estimator of average treatment effects are studied. The proposed methods are applied to a nutritional study, where the covariate dimension is reduced from 11 to an effective dimension of one.