{"title":"基于近邻匹配的估算:从密度比到平均治疗效果","authors":"Zhexiao Lin, Peng Ding, Fang Han","doi":"10.3982/ECTA20598","DOIUrl":null,"url":null,"abstract":"<p>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, <i>M</i> fixed. We reveal something new out of their study and show that once allowing <i>M</i> 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 <i>M</i>, 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.</p>","PeriodicalId":50556,"journal":{"name":"Econometrica","volume":null,"pages":null},"PeriodicalIF":6.6000,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Estimation Based on Nearest Neighbor Matching: From Density Ratio to Average Treatment Effect\",\"authors\":\"Zhexiao Lin, Peng Ding, Fang Han\",\"doi\":\"10.3982/ECTA20598\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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, <i>M</i> fixed. We reveal something new out of their study and show that once allowing <i>M</i> 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 <i>M</i>, 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.</p>\",\"PeriodicalId\":50556,\"journal\":{\"name\":\"Econometrica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.6000,\"publicationDate\":\"2023-12-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Econometrica\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.3982/ECTA20598\",\"RegionNum\":1,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Econometrica","FirstCategoryId":"96","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.3982/ECTA20598","RegionNum":1,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
摘要
近邻匹配(NN)被广泛应用于因果效应的观察研究中。Abadie 和 Imbens(2006 年)首次对近邻匹配进行了大样本分析。他们的理论侧重于近邻数量 M 固定的情况。我们从他们的研究中发现了一些新的东西,并证明一旦允许 M 随样本量的变化而变化,他们分析中的一个固有统计量就构成了对治疗组和对照组协变量密度比的一致估计。因此,在 M 发散的情况下,使用 Abadie 和 Imbens(2011 年)的偏差校正进行 NN 匹配,可以得到平均治疗效果的双重稳健估计值,而且如果密度函数足够平滑且结果模型的估计结果一致,则该估计值具有半参数效率。因此,可以将其视为双重机器学习估计器的前身。
Estimation Based on Nearest Neighbor Matching: From Density Ratio to Average Treatment Effect
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.
期刊介绍:
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