A0916
Title: Root-n consistent semiparametric learning with high-dimensional nuisance functions under minimal sparsity
Authors: Yuhao Wang - Tsinghua University and Shanghai Qi Zhi Institute (China) [presenting]
Lin Liu - Shanghai Jiao Tong University (China)
Abstract: Treatment effect estimation under unconfoundedness is a fundamental task in causal inference. In response to the challenge of analyzing high-dimensional datasets collected in substantive fields such as epidemiology, genetics, economics, and social sciences, many methods for treatment effect estimation with high-dimensional nuisance parameters (the outcome regression and the propensity score) have been developed in recent years. However, it is still unclear what the necessary and sufficient sparsity condition on the nuisance parameters for the treatment effect to be $\sqrt{n}$-estimable. A new Double-Calibration strategy that corrects the estimation bias of the nuisance parameter estimates computed by regularized high-dimensional techniques is proposed. The corresponding Doubly-Calibrated estimator is demonstrated to achieve $1/\sqrt{n}$ rate as long as one of the nuisance parameters is sparse with sparsity below $\sqrt{n} / \log p$, where p denotes the ambient dimension of the covariates. In contrast, the other nuisance parameter can be arbitrarily complex and completely misspecified. The Double-Calibration strategy can also be applied to settings other than treatment effect estimation, e.g. regression coefficient estimation in the presence of a diverging number of controls in a semiparametric partially linear model.
