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

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.

Automated summary

Randomized experiments are important in empirical research. Covariate adjustment improves efficiency without assuming a correctly specified outcome model in modern applications. The study of covariate adjustment under the potential outcomes model proposes a bias-corrected estimator that is consistent and asymptotically normal under weaker conditions, based purely on randomization without any parametric outcome model assumptions. To prove the theoretical results, novel vector and matrix concentration inequalities for sampling without replacement are developed.