In two influential contributions, Rosenbaum (2005, 2020) advocated for using the distances between component-wise ranks, instead of the original data values, to measure covariate similarity when constructing matching estimators of average treatment effects. While the intuitive benefits of using covariate ranks for matching estimation are apparent, there is no theoretical understanding of such procedures in the literature. We fill this gap by demonstrating that Rosenbaum's rank-based matching estimator, when coupled with a regression adjustment, enjoys the properties of double robustness and semiparametric efficiency without the need to enforce restrictive covariate moment assumptions. Our theoretical findings further emphasize the statistical virtues of employing ranks for estimation and inference, more broadly aligning with the insights put forth by Peter Bickel in his 2004 Rietz lecture (Bickel, 2004).

翻译：在两篇具有影响力的文献中，Rosenbaum（2005, 2020）提出在构建平均处理效应的匹配估计量时，应使用分量秩之间的距离而非原始数据值来衡量协变量相似性。尽管使用协变量秩进行匹配估计的直观优势显而易见，但现有文献对此类程序缺乏理论理解。我们通过证明Rosenbaum基于秩的匹配估计量在搭配回归调整后，无需施加严格的协变量矩条件假设，即可具备双重稳健性和半参数有效性，从而填补了这一理论空白。我们的理论发现进一步凸显了在估计与推断中使用秩的统计优势，这与Peter Bickel在2004年Rietz讲座（Bickel, 2004）中提出的见解高度契合。