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Bridging Root-$n$ and Non-standard Asymptotics: Dimension-agnostic Adaptive Inference in M-Estimation

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  • Kenta Takatsu
  • Arun Kumar Kuchibhotla

Abstract

This manuscript studies a general approach to construct confidence sets for the solution of population-level optimization, commonly referred to as M-estimation. Statistical inference for M-estimation poses significant challenges due to the non-standard limiting behaviors of the corresponding estimator, which arise in settings with increasing dimension of parameters, non-smooth objectives, or constraints. We propose a simple and unified method that guarantees validity in both regular and irregular cases. Moreover, we provide a comprehensive width analysis of the proposed confidence set, showing that the convergence rate of the diameter is adaptive to the unknown degree of instance-specific regularity. We apply the proposed method to several high-dimensional and irregular statistical problems.

Suggested Citation

  • Kenta Takatsu & Arun Kumar Kuchibhotla, 2025. "Bridging Root-$n$ and Non-standard Asymptotics: Dimension-agnostic Adaptive Inference in M-Estimation," Papers 2501.07772, arXiv.org, revised Feb 2025.
    • Handle: RePEc:arx:papers:2501.07772
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    References listed on IDEAS

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    1. Ketz, Philipp, 2018. "Subvector inference when the true parameter vector may be near or at the boundary," Journal of Econometrics, Elsevier, vol. 207(2), pages 285-306.
    2. 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.
    3. 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.
    4. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
    5. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    6. Matias D Cattaneo & Michael Jansson & Xinwei Ma, 2019. "Two-Step Estimation and Inference with Possibly Many Included Covariates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(3), pages 1095-1122.
    7. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP," Econometric Theory, Cambridge University Press, vol. 26(2), pages 426-468, April.
    8. Matias D. Cattaneo & Michael Jansson & Kenichi Nagasawa, 2023. "Bootstrap-Assisted Inference for Generalized Grenander-type Estimators," Papers 2303.13598, arXiv.org, revised Jul 2024.
    9. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    10. Patra, Rohit Kumar & Seijo, Emilio & Sen, Bodhisattva, 2018. "A consistent bootstrap procedure for the maximum score estimator," Journal of Econometrics, Elsevier, vol. 205(2), pages 488-507.
    11. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
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