  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).
