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

Abstract

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 purely randomization-based without imposing any parametric outcome model assumptions. To prove the theoretical results, we develop novel vector and matrix concentration inequalities for sampling without replacement.

Accepted by Biometrika; 59 pages

References in corpus (5)

• Agnostic notes on regression adjustments to experimental data: Reexamining Freedman's critique
• Lasso adjustments of treatment effect estimates in randomized experiments
• High-dimensional regression adjustments in randomized experiments
• Transductive Rademacher Complexity and its Applications
• Stability Analysis and Learning Bounds for Transductive Regression Algorithms

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• Regression Discontinuity Design with Potentially Many Covariates
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• Design-Based Confidence Sequences: A General Approach to Risk Mitigation in Panel Experiments
• Robust and Efficient Estimation of Potential Outcome Means under Random Assignment
• On High Dimensional Covariate Adjustment for Estimating Causal Effects in Randomized Trials with Survival Outcomes
• A robust score test in g-computation for covariate adjustment in randomized clinical trials leveraging different variance estimators via influence functions