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Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates via Generalized Riesz Regression

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  • Masahiro Kato

Abstract

This study investigates treatment effect estimation in the semi-supervised setting, where we can use not only the standard triple of covariates, treatment indicator, and outcome, but also unlabeled auxiliary covariates. For this problem, we develop efficiency bounds and efficient estimators whose asymptotic variance aligns with the efficiency bound. In the analysis, we introduce two different data-generating processes: the one-sample setting and the two-sample setting. The one-sample setting considers the case where we can observe treatment indicators and outcomes for a part of the dataset, which is also called the censoring setting. In contrast, the two-sample setting considers two independent datasets with labeled and unlabeled data, which is also called the case-control setting or the stratified setting. In both settings, we find that by incorporating auxiliary covariates, we can lower the efficiency bound and obtain an estimator with an asymptotic variance smaller than that without such auxiliary covariates.

Suggested Citation

  • Masahiro Kato, 2025. "Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates via Generalized Riesz Regression," Papers 2511.08303, arXiv.org.
    • Handle: RePEc:arx:papers:2511.08303
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    1. David Azriel & Lawrence D. Brown & Michael Sklar & Richard Berk & Andreas Buja & Linda Zhao, 2022. "Semi-Supervised Linear Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(540), pages 2238-2251, October.
    2. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    3. Imai, Kosuke & Strauss, Aaron, 2011. "Estimation of Heterogeneous Treatment Effects from Randomized Experiments, with Application to the Optimal Planning of the Get-Out-the-Vote Campaign," Political Analysis, Cambridge University Press, vol. 19(1), pages 1-19, January.
    4. Kennedy Edward H., 2020. "Efficient Nonparametric Causal Inference with Missing Exposure Information," The International Journal of Biostatistics, De Gruyter, vol. 16(1), pages 1-11, May.
    5. Stefan Wager & Susan Athey, 2018. "Estimation and Inference of Heterogeneous Treatment Effects using Random Forests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1228-1242, July.
    6. Ruohan Zhan & Zhimei Ren & Susan Athey & Zhengyuan Zhou, 2024. "Policy Learning with Adaptively Collected Data," Management Science, INFORMS, vol. 70(8), pages 5270-5297, August.
    7. Hainmueller, Jens, 2012. "Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies," Political Analysis, Cambridge University Press, vol. 20(1), pages 25-46, January.
    8. Zhexiao Lin & Peng Ding & Fang Han, 2023. "Estimation Based on Nearest Neighbor Matching: From Density Ratio to Average Treatment Effect," Econometrica, Econometric Society, vol. 91(6), pages 2187-2217, November.
    9. Masahiro Kato, 2025. "Direct Bias-Correction Term Estimation for Propensity Scores and Average Treatment Effect Estimation," Papers 2509.22122, arXiv.org.
    10. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    11. Imbens, Guido W. & Lancaster, Tony, 1996. "Efficient estimation and stratified sampling," Journal of Econometrics, Elsevier, vol. 74(2), pages 289-318, October.
    12. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, January.
    13. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    14. Kennedy Edward H., 2020. "Efficient Nonparametric Causal Inference with Missing Exposure Information," The International Journal of Biostatistics, De Gruyter, vol. 16(1), pages 1-11, May.
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