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Abstract:
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This paper studies how to infer the average treatment effect (ATE) in observational studies, where the number of pre-treatment covariates is much larger than the sample size. To account for the treatment assignment, we exploit the classical Horvitz-Thompson estimator. The key idea is that, the high dimensional propensity score model is carefully estimated to attain a weak covariate balancing property, which relaxes the existing balancing method in the fixed dimensional case (Imai and Ratkovic, 2014). In addition, we extend the covariate balancing method to a more general setting where the outcome models follow the generalized linear models. We show that, in high dimensions, the resulting estimator of ATE is sample bounded, root-n consistent, asymptotically normal and semiparametrically efficient. Moreover, the estimator has the same influence function even under misspecified propensity score models in high dimensions. The asymptotic results are fully supported by the results of empirical studies, which include extensive simulation studies and real data analysis that compare the performance of the proposed estimator with other existing methods.
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