Weighting methods are used in observational studies to adjust for covariate imbalances between treatment and control groups. Entropy balancing (EB) is an alternative to inverse probability weighting with an estimated propensity score. The EB weights are constructed to satisfy balance constraints and optimized towards stability. We describe large sample properties of EB estimators of the average causal treatment effect, based on the Kullback-Leibler and quadratic R\'enyi relative entropies. Additionally, we propose estimators of their asymptotic variances. Even though the objective of EB is to reduce model dependence, the estimators are generally not consistent unless implicit parametric assumptions for the propensity score or conditional outcomes are met. The finite sample properties of the estimators are investigated through a simulation study. In an application with observational data from the Swedish Childhood Diabetes Register, we estimate the average effect of school achievements on hospitalization due to acute complications of type 1 diabetes mellitus.

翻译：在观察研究中使用了加权方法,以适应治疗和控制组群之间的共变不平衡。 Entropy 平衡(EB)是用估计性能分数来替代反概率加权的替代物。EB加权的构建是为了满足平衡限制,并优化稳定。我们根据Kullback-Leibel 和 quedric R\'enyi 相对病原体,描述了EB平均因果治疗效果估计器的大量抽样特性。此外,我们提议了估计其无症状差异的估算器。尽管EB的目的是减少模型依赖性,但估计器一般不一致,除非满足了对偏度分或有条件结果的隐含参数假设。通过模拟研究对估计器的有限抽样特性进行了调查。在应用瑞典儿童糖尿病登记册的观察数据时,我们估计了学校成绩对因1型糖尿病急性并发症住院的平均影响。