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Regression adjustment in completely randomized experiments with a diverging number of covariates
[Covariance adjustments for the analysis of randomized field experiments]

Author

Listed:
  • Lihua Lei
  • Peng Ding

Abstract

SummaryRandomized 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.

Suggested Citation

  • Lihua Lei & Peng Ding, 2021. "Regression adjustment in completely randomized experiments with a diverging number of covariates [Covariance adjustments for the analysis of randomized field experiments]," Biometrika, Biometrika Trust, vol. 108(4), pages 815-828.
    • Handle: RePEc:oup:biomet:v:108:y:2021:i:4:p:815-828.
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    File URL: http://hdl.handle.net/10.1093/biomet/asaa103
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    Citations

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    Cited by:

    1. Fangzhou Su & Peng Ding, 2021. "Model‐assisted analyses of cluster‐randomized experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 994-1015, November.
    2. Myung Hwan Seo & Yoichi Arai & Taisuke Otsu, 2021. "Regression Discontinuity Design with Potentially Many Covariates," Working Paper Series no142, Institute of Economic Research, Seoul National University.
    3. Jiang, Liang & Phillips, Peter C.B. & Tao, Yubo & Zhang, Yichong, 2023. "Regression-adjusted estimation of quantile treatment effects under covariate-adaptive randomizations," Journal of Econometrics, Elsevier, vol. 234(2), pages 758-776.
    4. Liang Jiang & Liyao Li & Ke Miao & Yichong Zhang, 2023. "Adjustment with Many Regressors Under Covariate-Adaptive Randomizations," Papers 2304.08184, arXiv.org, revised Feb 2024.
    5. Ran Dai & Cheng Zheng & Mei-Jie Zhang, 2023. "On High-Dimensional Covariate Adjustment for Estimating Causal Effects in Randomized Trials with Survival Outcomes," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 242-260, April.
    6. Haoge Chang, 2023. "Design-based Estimation Theory for Complex Experiments," Papers 2311.06891, arXiv.org.
    7. Liang Jiang & Oliver B. Linton & Haihan Tang & Yichong Zhang, 2022. "Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance," Papers 2201.13004, arXiv.org, revised Jun 2023.
    8. Lihua Lei, 2024. "Causal Interpretation of Regressions With Ranks," Papers 2406.05548, arXiv.org.
    9. Ke Zhu & Hanzhong Liu, 2023. "Pair‐switching rerandomization," Biometrics, The International Biometric Society, vol. 79(3), pages 2127-2142, September.
    10. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2023. "Regression adjustment in randomized controlled trials with many covariates," Papers 2302.00469, arXiv.org, revised Nov 2023.
    11. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2023. "Regression adjustment in randomized controlled trials with many covariates," STICERD - Econometrics Paper Series 627, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    12. Fang Han, 2024. "An Introduction to Permutation Processes (version 0.5)," Papers 2407.09664, arXiv.org.

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