A matching-and-regression estimator for group average treatment effects is shown consistent, doubly robust, and asymptotically normal, with a bias-corrected version that avoids inverse propensity weighting.
According to the Lemma 2 in Abadie and Imbens Abadie and Imbens (2006), under the uncon- foundednes Assumption and Assumption 2, sup Xi∈X |{µ1−Ai(Xi) − µ1−Ai(Xjm(i))| = Op(N −1/p)
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Matching-Based Nonparametric Estimation of Group Average Treatment Effects
A matching-and-regression estimator for group average treatment effects is shown consistent, doubly robust, and asymptotically normal, with a bias-corrected version that avoids inverse propensity weighting.