Causal inference problems have remained an important research topic over the past several decades due to their general applicability in assessing a treatment effect in many different real-world settings. In this paper, we propose two inferential procedures on the average treatment effect (ATE) through a two-sample pseudo-empirical likelihood (PEL) approach. The first procedure uses the estimated propensity scores for the formulation of the PEL function, and the resulting maximum PEL estimator of the ATE is equivalent to the inverse probability weighted estimator discussed in the literature. Our focus in this scenario is on the PEL ratio statistic and establishing its theoretical properties. The second procedure incorporates outcome regression models for PEL inference through model-calibration constraints, and the resulting maximum PEL estimator of the ATE is doubly robust. Our main theoretical result in this case is the establishment of the asymptotic distribution of the PEL ratio statistic. We also propose a bootstrap method for constructing PEL ratio confidence intervals for the ATE to bypass the scaling constant which is involved in the asymptotic distribution of the PEL ratio statistic but is very difficult to calculate. Finite sample performances of our proposed methods with comparisons to existing ones are investigated through simulation studies.

翻译：因果推断问题在过去几十年中一直是重要的研究课题，因其在评估多种现实场景中处理效应的普遍适用性。本文通过双样本伪经验似然方法，提出两种关于平均处理效应的推断程序。第一种程序利用估计的倾向得分构造伪经验似然函数，得到的平均处理效应最大伪经验似然估计量等价于文献中讨论的逆概率加权估计量。此情形下我们的重点在于伪经验似然比统计量及其理论性质的建立。第二种程序通过模型校准约束将结果回归模型纳入伪经验似然推断，得到的平均处理效应最大伪经验似然估计量具有双重稳健性。此情形下我们的主要理论结果是建立了伪经验似然比统计量的渐近分布。我们还提出一种自举法来构建平均处理效应的伪经验似然比置信区间，以绕过伪经验似然比统计量渐近分布中涉及但极难计算的缩放常数。通过模拟研究，我们考察了所提方法在有限样本中的表现，并与现有方法进行了比较。