A Unified Approach for Estimating Various Treatment Effects in Causal Inference

In this paper, we introduce a unified estimator to analyze various treatment effects in causal inference, including but not limited to the average treatment effect (ATE) and the quantile treatment effect (QTE). The proposed estimator is developed under the statistical functional and cumulative distribution function structure, which leads to a flexible and robust estimator and covers some frequent treatment effects. In addition, our approach also takes variable selection into account, so that informative and network structure in confounders can be identified and be implemented in our estimation procedure. The theoretical properties, including variable selection consistency and asymptotic normality of the statistical functional estimator, are established. Various treatment effects estimations are also conducted in numerical studies, and the results reveal that the proposed estimator generally outperforms the existing methods and is more efficient than its competitors.