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Bootstrap‐Based Inference for Cube Root Asymptotics

Author

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  • Cattaneo, Matias D
  • Jansson, Michael
  • Nagasawa, Kenichi

Abstract

This paper proposes a valid bootstrap-based distributional approximation for M-estimators exhibiting a Chernoff (1964)-type limiting distribution. For estimators of this kind, the standard nonparametric bootstrap is inconsistent. The method proposed herein is based on the nonparametric bootstrap, but restores consistency by altering the shape of the criterion function defining the estimator whose distribution we seek to approximate. This modification leads to a generic and easy-to-implement resampling method for inference that is conceptually distinct from other available distributional approximations. We illustrate the applicability of our results with four examples in econometrics and machine learning.

Suggested Citation

  • Cattaneo, Matias D & Jansson, Michael & Nagasawa, Kenichi, 2020. "Bootstrap‐Based Inference for Cube Root Asymptotics," Department of Economics, Working Paper Series qt3wn9z3b9, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    • Handle: RePEc:cdl:econwp:qt3wn9z3b9
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    Cited by:

    1. Xiaohong Chen & Wayne Yuan Gao & Likang Wen, 2025. "ReLU-Based and DNN-Based Generalized Maximum Score Estimators," Cowles Foundation Discussion Papers 2476, Cowles Foundation for Research in Economics, Yale University.
    2. Giuseppe Cavaliere & Iliyan Georgiev, 2020. "Inference Under Random Limit Bootstrap Measures," Econometrica, Econometric Society, vol. 88(6), pages 2547-2574, November.
    3. Federico Crippa, 2024. "Regret Analysis in Threshold Policy Design," Papers 2404.11767, arXiv.org, revised Apr 2025.
    4. Nan Liu & Yanbo Liu & Yuya Sasaki & Yuanyuan Wan, 2025. "Nonparametric Uniform Inference in Binary Classification and Policy Values," Working Papers tecipa-811, University of Toronto, Department of Economics.
    5. Luofeng Liao & Christian Kroer, 2024. "Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium," Papers 2402.02303, arXiv.org, revised Mar 2025.
    6. Christopher R. Dobronyi & Fu Ouyang & Thomas Tao Yang, 2023. "Revisiting Panel Data Discrete Choice Models with Lagged Dependent Variables," Papers 2301.09379, arXiv.org, revised Aug 2024.
    7. Leon Tran & Ting Ye & Peng Ding & Fang Han, 2026. "Generative modeling for the bootstrap," Papers 2602.17052, arXiv.org.
    8. Crippa, Federico, 2025. "Regret analysis in threshold policy design," Journal of Econometrics, Elsevier, vol. 249(PB).
    9. Dominic Coey & Bradley J. Larsen & Kane Sweeney & Caio Waisman, 2021. "Scalable Optimal Online Auctions," Marketing Science, INFORMS, vol. 40(4), pages 593-618, July.
    10. Firpo, Sergio & Galvao, Antonio F. & Parker, Thomas, 2023. "Uniform inference for value functions," Journal of Econometrics, Elsevier, vol. 235(2), pages 1680-1699.
    11. Firpo, Sergio & Galvao, Antonio F. & Kobus, Martyna & Parker, Thomas & Rosa-Dias, Pedro, 2025. "Loss aversion and the welfare ranking of policy interventions," Journal of Econometrics, Elsevier, vol. 252(PB).
    12. Shakeeb Khan & Fu Ouyang & Elie Tamer, 2021. "Inference on semiparametric multinomial response models," Quantitative Economics, Econometric Society, vol. 12(3), pages 743-777, July.
    13. Djogbenou, Antoine A. & Hounyo, Ulrich, 2025. "Misspecification-robust bootstrap t-test for irrelevant factor in linear stochastic discount factor models," Journal of Econometrics, Elsevier, vol. 252(PA).
    14. Fu Ouyang & Thomas Tao Yang, 2022. "Semiparametric Estimation of Dynamic Binary Choice Panel Data Models," Papers 2202.12062, arXiv.org, revised Feb 2024.
    15. Babii, Andrii & Kumar, Rohit, 2023. "Isotonic regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 234(2), pages 371-393.
    16. Kenta Takatsu & Arun Kumar Kuchibhotla, 2025. "Bridging Root-$n$ and Non-standard Asymptotics: Adaptive Inference in M-Estimation," Papers 2501.07772, arXiv.org, revised Apr 2025.
    17. Xiaohong Chen & Wayne Yuan Gao & Likang Wen, 2025. "ReLU-Based and DNN-Based Generalized Maximum Score Estimators," Papers 2511.19121, arXiv.org.

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