Many causal estimands are only partially identifiable since they depend on the unobservable joint distribution between potential outcomes. Stratification on pretreatment covariates can yield sharper partial identification bounds; however, unless the covariates are discrete with relatively small support, this approach typically requires consistent estimation of the conditional distributions of the potential outcomes given the covariates. Thus, existing approaches may fail under model misspecification or if consistency assumptions are violated. In this study, we propose a unified and model-agnostic inferential approach for a wide class of partially identified estimands, based on duality theory for optimal transport problems. In randomized experiments, our approach can wrap around any estimates of the conditional distributions and provide uniformly valid inference, even if the initial estimates are arbitrarily inaccurate. Also, our approach is doubly robust in observational studies. Notably, this property allows analysts to use the multiplier bootstrap to select covariates and models without sacrificing validity even if the true model is not included. Furthermore, if the conditional distributions are estimated at semiparametric rates, our approach matches the performance of an oracle with perfect knowledge of the outcome model. Finally, we propose an efficient computational framework, enabling implementation on many practical problems in causal inference.

翻译：许多因果估计量仅能实现部分识别，因其依赖于潜在结果之间不可观测的联合分布。基于预处理协变量的分层可得到更尖锐的部分识别界，但除非协变量离散且支撑集较小，该方法通常需一致估计给定协变量下潜在结果的条件分布。因此，现有方法可能因模型误设或一致性假设不成立而失效。本研究基于最优输运问题的对偶理论，针对一类广泛的部分识别估计量提出统一的模型无关推断方法。在随机实验中，该方法可封装任何条件分布估计量，即便初始估计存在任意偏差仍能提供一致有效推断。在观察性研究中，该方法具有双重稳健性。值得注意的是，该性质允许分析者使用乘子自助法选择协变量与模型，即便真实模型未被纳入仍不损害推断有效性。此外，若条件分布以半参数速率估计，该方法可达到完全知晓结果模型的理想表现。最后，我们提出高效计算框架，使其能应用于因果推断中的诸多实际问题。