Covariate Balancing by Uniform Transformer

In observational studies, it is important to balance covariates in different treatment groups in order to estimate treatment effects. One of the most commonly used methods for such purpose is the weighting method. The performance quality of this method usually depends on either the correct model specification for the propensity score or strong regularity conditions for the underlying model, which might not hold in practice. In this paper, we introduce a new robust and computationally efficient framework of weighting methods for covariate balancing, which allows us to conduct model-free inferences for the sake of robustness and integrate an extra `unlabeled' data set if available. Unlike existing methods, the new framework reduces the weights construction problem to a classical density estimation problem by applying a data-driven transformation to the observed covariates. We characterize the theoretical properties of the new estimators of average treatment effect under a nonparametric setting and show that they are able to work robustly under low regularity conditions. The new framework i s also applied to several numerical examples using both simulated and real datasets to demonstrate its practical merits.