2018/06/30 by Lihua Lei, Peng Ding · 41 citations
Mathematics · #Advanced Causal Inference Techniques #Covariate #Econometrics #Estimator #Mathematical economics #Mathematics #Outcome (game theory) #Parametric statistics #Randomized experiment #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics #math.ST #msc:62E20 #msc:62J05 #stat.TH
paper · pdf · doi:10.1093/biomet/asaa103
published in Biometrika 108(4), 815-828 (Oxford University Press) · Accepted by Biometrika; 59 pages
openalex created_date 2019/03/11 · openalex publication_date 2020/12/01 · arxiv created 2020/12/31 · arxiv updated 2021/01/01 · openalex updated_date 2026/08/05
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.