Causal inference is crucial for understanding the true impact of interventions, policies, or actions, enabling informed decision-making and providing insights into the underlying mechanisms that shape our world. In this paper, we establish a framework for the estimation and inference of average treatment effects using a two-sample empirical likelihood function. Two different approaches to incorporating propensity scores are developed. The first approach introduces propensity scores calibrated constraints in addition to the standard model-calibration constraints; the second approach uses the propensity scores to form weighted versions of the model-calibration constraints. The resulting estimators from both approaches are doubly robust. The limiting distributions of the two sample empirical likelihood ratio statistics are derived, facilitating the construction of confidence intervals and hypothesis tests for the average treatment effect. Bootstrap methods for constructing sample empirical likelihood ratio confidence intervals are also discussed for both approaches. Finite sample performances of the methods are investigated through simulation studies.

翻译：因果推断对于理解干预、政策或行动的真实影响至关重要，它能够支持明智决策，并揭示塑造世界的内在机制。本文建立了一个利用双样本经验似然函数进行平均处理效应估计与推断的框架。针对倾向得分的整合，我们提出了两种不同方法：第一种方法在标准模型校准约束之外，引入了倾向得分校准约束；第二种方法则利用倾向得分构建模型校准约束的加权版本。由此得出的两种估计量均具有双重稳健性。我们推导了双样本经验似然比统计量的极限分布，从而为平均处理效应的置信区间构建和假设检验提供了便利。此外，还讨论了两种方法下利用自助法构建样本经验似然比置信区间的实现策略。通过模拟研究，我们考察了这些方法在有限样本中的表现。