Summary

Randomized experiments have become important tools in empirical research. In a completely randomized treatment-control experiment, the simple difference in means of the outcome is un- biased for the average treatment effect, and covariate adjustment can further improve the efficiency without assuming a correctly specified outcome model. In modern applications, experimenters often have access to many covariates, motivating the need for a theory of covariate adjustment under the asymptotic regime with a diverging number of covariates. We study the asymptotic properties of covariate adjustment under the potential outcomes model and propose a bias-corrected estimator that is consistent and asymptotically normal under weaker conditions. Our theory is based purely on randomization without imposing any parametric outcome model assumptions. To prove the theoretical results, we develop novel vector and matrix concentration inequalities for sampling without replacement.

中文翻译：

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具有不同数量协变量的完全随机实验中的回归调整

概括

随机实验已成为实证研究的重要工具。在完全随机的治疗-对照实验中，结果均值的简单差异对平均治疗效果没有偏差，协变量调整可以进一步提高效率，而无需假设正确指定的结果模型。在现代应用中，实验者通常可以访问许多协变量，这激发了对具有不同数量协变量的渐近状态下的协变量调整理论的需求。我们研究了潜在结果模型下协变量调整的渐近特性，并提出了一个在较弱条件下一致且渐近正常的偏差校正估计量。我们的理论纯粹基于随机化，没有强加任何参数结果模型假设。