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Bootstrap‐Based Inference for Cube Root Asymptotics

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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. 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.
    2. Crippa, Federico, 2025. "Regret analysis in threshold policy design," Journal of Econometrics, Elsevier, vol. 249(PB).
    3. Dominic Coey & Bradley J. Larsen & Kane Sweeney & Caio Waisman, 2021. "Scalable Optimal Online Auctions," Marketing Science, INFORMS, vol. 40(4), pages 593-618, July.
    4. Shakeeb Khan & Fu Ouyang & Elie Tamer, 2021. "Inference on semiparametric multinomial response models," Quantitative Economics, Econometric Society, vol. 12(3), pages 743-777, July.
    5. Fu Ouyang & Thomas Tao Yang, 2022. "Semiparametric Estimation of Dynamic Binary Choice Panel Data Models," Papers 2202.12062, arXiv.org, revised Feb 2024.

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