This paper proposes a simple method for balancing distributions of covariates for causal inference based on observational studies. The method makes it possible to balance an arbitrary number of quantiles (e.g., medians, quartiles, or deciles) together with means if necessary. The proposed approach is based on the theory of calibration estimators (Deville and S\"arndal 1992), in particular, calibration estimators for quantiles, proposed by Harms and Duchesne (2006). By modifying the entropy balancing method and the covariate balancing propensity score method, it is possible to balance the distributions of the treatment and control groups. The method does not require numerical integration, kernel density estimation or assumptions about the distributions; valid estimates can be obtained by drawing on existing asymptotic theory. Results of a simulation study indicate that the method efficiently estimates average treatment effects on the treated (ATT), the average treatment effect (ATE), the quantile treatment effect on the treated (QTT) and the quantile treatment effect (QTE), especially in the presence of non-linearity and mis-specification of the models. The proposed methods are implemented in an open source R package jointCalib.

翻译：本文提出了一种基于观察性研究的简单方法，用于平衡协变量分布以进行因果推断。该方法能够在必要时同时平衡任意数量的分位数（例如中位数、四分位数或十分位数）以及均值。所提出的方法基于校准估计量理论（Deville 和 Särndal，1992），特别是 Harms 和 Duchesne（2006）提出的分位数校准估计量。通过修改熵平衡方法和协变量平衡倾向得分方法，可以实现处理组和对照组的分布平衡。该方法无需数值积分、核密度估计或分布假设；利用现有的渐近理论即可获得有效估计。模拟研究结果表明，该方法能高效估计处理组的平均处理效应（ATT）、平均处理效应（ATE）、处理组的分位数处理效应（QTT）以及分位数处理效应（QTE），尤其是在模型存在非线性和错误设定的情况下。所提方法已在开源 R 包 jointCalib 中实现。