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Bootstrap‐Based Inference for Cube Root Asymptotics

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  • Matias D. Cattaneo
  • Michael Jansson
  • Kenichi Nagasawa

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

  • Matias D. Cattaneo & Michael Jansson & Kenichi Nagasawa, 2020. "Bootstrap‐Based Inference for Cube Root Asymptotics," Econometrica, Econometric Society, vol. 88(5), pages 2203-2219, September.
    • Handle: RePEc:wly:emetrp:v:88:y:2020:i:5:p:2203-2219
    DOI: 10.3982/ECTA17950
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    References listed on IDEAS

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    Citations

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    Cited by:

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    6. Babii, Andrii & Kumar, Rohit, 2023. "Isotonic regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 234(2), pages 371-393.
    7. Luofeng Liao & Christian Kroer, 2024. "Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium," Papers 2402.02303, arXiv.org, revised Mar 2025.
    8. Leon Tran & Ting Ye & Peng Ding & Fang Han, 2026. "Generative modeling for the bootstrap," Papers 2602.17052, arXiv.org.
    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. Shakeeb Khan & Fu Ouyang & Elie Tamer, 2021. "Inference on semiparametric multinomial response models," Quantitative Economics, Econometric Society, vol. 12(3), pages 743-777, July.
    11. Nan Liu & Yanbo Liu & Yuya Sasaki & Yuanyuan Wan, 2026. "Root-$n$ Asymptotically Normal Maximum Score Estimation," Papers 2604.13399, arXiv.org.
    12. 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.
    13. Federico Crippa, 2024. "Regret Analysis in Threshold Policy Design," Papers 2404.11767, arXiv.org, revised Apr 2025.
    14. 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).
    15. Fu Ouyang & Thomas Tao Yang, 2022. "Semiparametric Estimation of Dynamic Binary Choice Panel Data Models," Papers 2202.12062, arXiv.org, revised Feb 2024.
    16. Xiaohong Chen & Wayne Yuan Gao & Likang Wen, 2025. "ReLU-Based and DNN-Based Generalized Maximum Score Estimators," Papers 2511.19121, arXiv.org.
    17. Giuseppe Cavaliere & Iliyan Georgiev, 2020. "Inference Under Random Limit Bootstrap Measures," Econometrica, Econometric Society, vol. 88(6), pages 2547-2574, November.
    18. Kenta Takatsu & Arun Kumar Kuchibhotla, 2025. "Honest Inference for Stochastic Optimization," Papers 2501.07772, arXiv.org, revised May 2026.

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