Pseudo-empirical likelihood methods for causal inference

Causal inference remains a key area of research for assessing treatment effects across various real-world settings. This paper introduces two inferential procedures for the average treatment effect (ATE) using a two-sample pseudo-empirical likelihood (PEL) approach. The first procedure uses estimated propensity scores for the formulation of the PEL function, yielding a maximum PEL estimator equivalent to the inverse probability weighted estimator. Our focus in this scenario is on the PEL ratio statistic and establishing its theoretical properties. The second procedure incorporates outcome regression models for doubly robust PEL inference. We establish the asymptotic distribution of the PEL ratio statistic and also propose a bootstrap method for constructing confidence intervals to bypass a scaling constant involved in the asymptotic distribution of the PEL ratio statistic that is very difficult to calculate. Simulation studies and an real data application illustrate the performance of our proposed methods with comparisons to existing ones.