The causal inference literature frequently focuses on estimating the mean of the potential outcome, whereas the quantiles of the potential outcome may carry important additional information. We propose a universal approach, based on the inverse estimating equations, to generalize a wide class of causal inference solutions from estimating the mean of the potential outcome to its quantiles. We assume that an identifying moment function is available to identify the mean of the threshold-transformed potential outcome, based on which a convenient construction of the estimating equation of quantiles of potential outcome is proposed. In addition, we also give a general construction of the efficient influence functions of the mean and quantiles of potential outcomes, and identify their connection. We motivate estimators for the quantile estimands with the efficient influence function, and develop their asymptotic properties when either parametric models or data-adaptive machine learners are used to estimate the nuisance functions. A broad implication of our results is that one can rework the existing result for mean causal estimands to facilitate causal inference on quantiles, rather than starting from scratch. Our results are illustrated by several examples.

翻译：因果推断文献通常关注潜在结果的均值估计，但潜在结果的分位数可能包含重要的附加信息。我们提出了一种基于逆向估计方程的通用方法，将广泛的因果推断解决方案从估计潜在结果均值推广到其分位数。假设存在可识别阈值变换后潜在结果均值的识别矩函数，并基于此提出潜在结果分位数估计方程的便捷构建方法。此外，我们给出了潜在结果均值与分位数的有效影响函数的一般构建方法，并明确了二者的关联。我们利用有效影响函数推导了分位数目标参数的估计量，并建立了在参数模型或数据自适应机器学习方法用于估计冗余函数时的渐近性质。本研究的一个重要意义在于：研究者无需从零开始，而是可以利用现有均值因果估计量的成果来推动分位数因果推断。我们的结果通过多个实例进行了说明。