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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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    1. Delgado, Miguel A. & Rodriguez-Poo, Juan M. & Wolf, Michael, 2001. "Subsampling inference in cube root asymptotics with an application to Manski's maximum score estimator," Economics Letters, Elsevier, vol. 73(2), pages 241-250, November.
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    7. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
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    Cited by:

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    6. Dominic Coey & Bradley J. Larsen & Kane Sweeney & Caio Waisman, 2021. "Scalable Optimal Online Auctions," Marketing Science, INFORMS, vol. 40(4), pages 593-618, July.
    7. Shakeeb Khan & Fu Ouyang & Elie Tamer, 2021. "Inference on semiparametric multinomial response models," Quantitative Economics, Econometric Society, vol. 12(3), pages 743-777, July.
    8. 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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