Open Access
2024 A unified analysis of regression adjustment in randomized experiments
Katarzyna Reluga, Ting Ye, Qingyuan Zhao
Author Affiliations +
Electron. J. Statist. 18(1): 1436-1454 (2024). DOI: 10.1214/24-EJS2233


Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand this phenomenon, we develop a unified comparison of the asymptotic variance of a class of linear regression-adjusted estimators. Our analysis is based on the classical theory for linear regression with heteroscedastic errors and thus does not assume that the postulated linear model is correct. For a randomized Bernoulli trial, we provide sufficient conditions under which some regression-adjusted estimators are guaranteed to be more asymptotically efficient than others. We comment on the extension of our theory to other settings such as general treatment mechanisms and generalized linear models, and find that the variance dominance phenomenon no longer occurs

Funding Statement

The first author gratefully acknowledge support from the Swiss National Science Foundation, project P2GEP2-195898.


The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper.


Download Citation

Katarzyna Reluga. Ting Ye. Qingyuan Zhao. "A unified analysis of regression adjustment in randomized experiments." Electron. J. Statist. 18 (1) 1436 - 1454, 2024.


Received: 1 October 2022; Published: 2024
First available in Project Euclid: 19 March 2024

arXiv: 2210.04360
Digital Object Identifier: 10.1214/24-EJS2233

Primary: 62F10
Secondary: 62J99

Keywords: Average treatment effect , covariate adjustment , Heteroscedasticity , Randomized controlled trials

Vol.18 • No. 1 • 2024
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