Regression adjustment in completely randomized experiments with a diverging number of covariates

• 成果类型: Article
• 署名作者: Lei, Lihua; Ding, Peng
• 署名单位: Stanford University; University of California System; University of California Berkeley
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaa103
• 发表日期: 2021
• 页码: 815828
• 关键词: robust regression; asymptotics; estimators

摘要

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 unbiased 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.