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Bootstrap consistency for general double/debiased machine learning estimators

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  • Ziming Lin
  • Fang Han

Abstract

Double/debiased machine learning (DML) provides a general framework for inference with high-dimensional or otherwise complex nuisance parameters by combining Neyman-orthogonal scores with cross-fitting, thereby circumventing classical Donsker-type conditions in many modern machine-learning settings. Despite its strong empirical performance, bootstrap inference for DML estimators has received little theoretical justification. This is particularly noteworthy since bootstrap methods are suggested ad used for inference on DML estimators, even though bootstrap procedures can fail for estimators that are root-$n$ consistent and asymptotically normal. This paper fills this gap by establishing bootstrap validity for DML estimators under general exchangeably weighted resampling schemes, with Efron's bootstrap as a special case. Under exactly the same conditions required for the validity of DML itself, we prove that the bootstrap law converges conditionally weakly to the sampling law of the original estimator.

Suggested Citation

  • Ziming Lin & Fang Han, 2026. "Bootstrap consistency for general double/debiased machine learning estimators," Papers 2604.17239, arXiv.org.
    • Handle: RePEc:arx:papers:2604.17239
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    References listed on IDEAS

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    1. Zhexiao Lin & Fang Han, 2024. "On the failure of the bootstrap for Chatterjee’s rank correlation," Biometrika, Biometrika Trust, vol. 111(3), pages 1063-1070.
    2. 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.
    3. Cai Weixin & van der Laan Mark, 2020. "Nonparametric bootstrap inference for the targeted highly adaptive least absolute shrinkage and selection operator (LASSO) estimator," The International Journal of Biostatistics, De Gruyter, vol. 16(2), pages 1-36, November.
    4. 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.
    5. Cai Weixin & van der Laan Mark, 2020. "Nonparametric bootstrap inference for the targeted highly adaptive least absolute shrinkage and selection operator (LASSO) estimator," The International Journal of Biostatistics, De Gruyter, vol. 16(2), pages 1-36, November.
    6. Alberto Abadie & Guido W. Imbens, 2008. "On the Failure of the Bootstrap for Matching Estimators," Econometrica, Econometric Society, vol. 76(6), pages 1537-1557, November.
    7. Lin, Zhexiao & Han, Fang, 2025. "On regression-adjusted imputation estimators of average treatment effects," Journal of Econometrics, Elsevier, vol. 251(C).
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