摘要翻译：
我们考虑了在不混淆性条件下对平均治疗效果的估计和推断，条件是治疗变量和协变量的实现。在给定结果变量的条件均值的非参数光滑性和/或形状限制下，当回归误差为正态且方差已知时，我们导出了有限样本中最优的估计量和置信区间(CIs)。与传统的CIs相比，我们的CIs使用了一个更大的临界值，明确地考虑了估计量的潜在偏差。当误差分布未知时，我们的CIs的可行版本是渐近有效的，即使由于缺乏重叠或条件均值的低光滑性而不可能进行$\sqrt{n}$-推断。我们还导出了$\sqrt{n}$-推理所必需的条件均值上的最小光滑性条件。当条件均值限制为Lipschitz且Lipschitz常数有足够大的界时，最优估计约化为匹配个数为1的匹配估计。我们在一个国家支持的工作示范的应用中说明了我们的方法。
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英文标题：
《Finite-Sample Optimal Estimation and Inference on Average Treatment
  Effects Under Unconfoundedness》
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作者：
Timothy B. Armstrong and Michal Koles\'ar
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最新提交年份：
2021
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分类信息：

一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
  We consider estimation and inference on average treatment effects under unconfoundedness conditional on the realizations of the treatment variable and covariates. Given nonparametric smoothness and/or shape restrictions on the conditional mean of the outcome variable, we derive estimators and confidence intervals (CIs) that are optimal in finite samples when the regression errors are normal with known variance. In contrast to conventional CIs, our CIs use a larger critical value that explicitly takes into account the potential bias of the estimator. When the error distribution is unknown, feasible versions of our CIs are valid asymptotically, even when $\sqrt{n}$-inference is not possible due to lack of overlap, or low smoothness of the conditional mean. We also derive the minimum smoothness conditions on the conditional mean that are necessary for $\sqrt{n}$-inference. When the conditional mean is restricted to be Lipschitz with a large enough bound on the Lipschitz constant, the optimal estimator reduces to a matching estimator with the number of matches set to one. We illustrate our methods in an application to the National Supported Work Demonstration.
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PDF链接：
https://arxiv.org/pdf/1712.04594