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Free, publicly-accessible full text available December 1, 2025
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Summary In two influential contributions, Rosenbaum (2005, 2020a) advocated for using the distances between componentwise 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.more » « less
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Abstract This paper re-examines the work of Abadie & Imbens (2016) on propensity score matching for average treatment effect estimation. We explore the asymptotic behaviour of these estimators when the number of nearest neighbours, M, grows with the sample size. It is shown, while not surprising, but technically nontrivial, that the modified estimators can improve upon the original fixed M-estimators in terms of efficiency. Additionally, we demonstrate the potential to attain the semiparametric efficiency lower bound when the propensity score admits some special structures, echoing the insight of Hahn (1998).more » « less
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Abstract While researchers commonly use the bootstrap to quantify the uncertainty of an estimator, it has been noticed that the standard bootstrap, in general, does not work for Chatterjee’s rank correlation. In this paper, we provide proof of this issue under an additional independence assumption, and complement our theory with simulation evidence for general settings. Chatterjee’s rank correlation thus falls into a category of statistics that are asymptotically normal, but bootstrap inconsistent. Valid inferential methods in this case are Chatterjee’s original proposal for testing independence and the analytic asymptotic variance estimator of Lin & Han (2022) for more general purposes. [Received on 5 April 2023. Editorial decision on 10 January 2024]more » « less
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Nearest neighbor (NN) matching is widely used in observational studies for causal effects. Abadie and Imbens (2006) provided the first large‐sample analysis of NN matching. Their theory focuses on the case with the number of NNs,Mfixed. We reveal something new out of their study and show that once allowingMto diverge with the sample size an intrinsic statistic in their analysis constitutes a consistent estimator of the density ratio with regard to covariates across the treated and control groups. Consequently, with a divergingM, the NN matching with Abadie and Imbens' (2011) bias correction yields a doubly robust estimator of the average treatment effect and is semiparametrically efficient if the density functions are sufficiently smooth and the outcome model is consistently estimated. It can thus be viewed as a precursor of the double machine learning estimators.more » « less
