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：在两项具有影响力的研究中，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，但文献中对此类过程缺乏理论理解。我们通过证明罗森鲍姆基于秩的匹配估计量在结合回归调整后，无需施加严格的协变量矩假设即可具备双重稳健性和半参数有效性，从而填补了这一空白。我们的理论发现进一步强调了使用秩进行估计与推断的统计优点，更广泛地契合了Peter Bickel在其2004年Rietz讲座中提出的见解（Bickel, 2004）。