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A Meta-Learning Approach for Estimating Heterogeneous Treatment Effects Under Hölder Continuity

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  • Zhihao Zhao

    (School of Statistics, Capital University of Economics and Business, Beijing 100070, China)

  • Congyang Zhou

    (School of Statistics, Capital University of Economics and Business, Beijing 100070, China)

Abstract

Estimating heterogeneous treatment effects plays a vital role in many statistical applications, such as precision medicine and precision marketing. In this paper, we propose a novel meta-learner, termed RXlearner for estimating the conditional average treatment effect (CATE) within the general framework of meta-algorithms. RXlearner enhances the weighting mechanism of the traditional Xlearner to improve estimation accuracy. We establish non-asymptotic error bounds for RXlearner under a continuity classification criterion, specifically assuming that the response function satisfies Hölder continuity. Moreover, we show that these bounds are achievable by selecting an appropriate base learner. The effectiveness of the proposed method is validated through extensive simulation studies and a real-world data experiment.

Suggested Citation

  • Zhihao Zhao & Congyang Zhou, 2025. "A Meta-Learning Approach for Estimating Heterogeneous Treatment Effects Under Hölder Continuity," Mathematics, MDPI, vol. 13(11), pages 1-25, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1739-:d:1663635
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    References listed on IDEAS

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    1. 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.
    2. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    3. Kosuke Imai & Marc Ratkovic, 2014. "Covariate balancing propensity score," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 243-263, January.
    4. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
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