A Statistical Functional Approach to Estimating Common Treatment Effects in Causal Inference

Estimation of treatment effects is one of crucial research problems in causal inference, and there are multiple treatment effects depending on the purpose of research targets or researchers’ interests, which include but are not limited to the average treatment effect (ATE) and the quantile treatment effect (QTE). In this study, we aim to propose 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 implemented in our estimation procedure. The theoretical properties, including variable selection consistency and asymptotic normality of the statistical functional estimator, are established. Some common 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.