Matching on covariates is a well-established framework for estimating causal effects in observational studies. The principal challenge stems from the often high-dimensional structure of the problem. Many methods have been introduced to address this, with different advantages and drawbacks in computational and statistical performance as well as interpretability. This article introduces a natural optimal matching method based on multimarginal unbalanced optimal transport that possesses many useful properties in this regard. It provides interpretable weights based on the distance of matched individuals, can be efficiently implemented via the iterative proportional fitting procedure, and can match several treatment arms simultaneously. Importantly, the proposed method only selects good matches from either group, hence is competitive with the classical k-nearest neighbors approach in terms of bias and variance in finite samples. Moreover, we prove a central limit theorem for the empirical process of the potential functions of the optimal coupling in the unbalanced optimal transport problem with a fixed penalty term. This implies a parametric rate of convergence of the empirically obtained weights to the optimal weights in the population for a fixed penalty term.
翻译:共变法是估算观察研究中因果关系的既定框架,主要挑战来自问题通常的高维结构。已经采用许多方法解决这一问题,计算和统计业绩以及可解释性方面优缺点各有不同。本条采用了基于多边不平衡的最佳运输方式的自然最佳匹配方法,这种方法在这方面具有许多有用的特性。它提供了基于相匹配个人的距离的可解释的权重,可以通过迭接比例搭配程序有效加以实施,同时可以匹配几种处理臂。重要的是,拟议方法只从任一组中选择好比,因此与传统的K最近邻方法相比,在定额抽样中的偏差和差异具有竞争力。此外,我们证明,在不平衡最佳运输问题中,以固定刑罚术语进行最佳组合的潜在功能的经验过程有一个核心限制。这意味着经验得出的重量与人口中固定刑罚期的最佳重量的相匹配率。