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, M fixed. We reveal something new out of their study and show that once allowing M to 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 diverging M, 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.

中文翻译：

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基于最近邻匹配的估计：从密度比到平均处理效果

最近邻 (NN) 匹配广泛用于因果效应的观察研究。Abadie 和 Imbens (2006) 首次提供了 NN 匹配的大样本分析。他们的理论侧重于神经网络数量M固定的情况。我们从他们的研究中揭示了一些新的东西，并表明一旦允许M随样本量的变化而变化，他们分析中的内在统计量就构成了治疗组和对照组协变量的密度比的一致估计量。因此，在M发散的情况下，与 Abadie 和 Imbens (2011) 偏差校正相匹配的 NN 会产生平均治疗效果的双重鲁棒估计量，并且如果密度函数足够平滑且结果模型得到一致估计，则具有半参数效率。因此，它可以被视为双机器学习估计器的先驱。