A1019
Title: Debiased regression adjustment in completely randomized experiments with moderately high-dimensional covariates
Authors: Xin Lu - Tsinghua University (China)
Fan Yang - Tsinghua University (China)
Yuhao Wang - Tsinghua University and Shanghai Qi Zhi Institute (China) [presenting]
Abstract: The completely randomized experiment is the gold standard for causal inference. When the covariate information is available, one typical way is to include them in covariate adjustments for more accurate estimation. This problem is investigated under the randomization-based framework. Under this framework, to achieve asymptotically valid inference, existing estimators usually require either (i) that the dimension of covariates p is much smaller than sample size n; or (ii) certain sparsity constraints on the linear representations of potential outcomes constructed via possibly high-dimensional covariates. The moderately high-dimensional regime is considered where p is allowed to be in the same order of magnitude as n. A novel debiased estimator is developed with a corresponding inference procedure, and its asymptotic normality is established under mild assumptions. The estimator is model-free and does not require any sparsity constraint on the potential outcome's linear representations. Its asymptotic efficiency improvements are also discussed over the unadjusted treatment effect estimator under different dimensionality constraints. Numerical analysis confirms that compared to other regression adjustment-based treatment effect estimators, the debiased estimator performs well in moderately high dimensions.
