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Selecting Penalty Parameters of High-Dimensional M-Estimators using Bootstrapping after Cross-Validation

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  • Denis Chetverikov
  • Jesper Riis-Vestergaard S{o}rensen

Abstract

We develop a new method for selecting the penalty parameter for $\ell_1$-penalized M-estimators in high dimensions, which we refer to as bootstrapping after cross-validation. We derive rates of convergence for the corresponding $\ell_1$-penalized M-estimator and also for the post-$\ell_1$-penalized M-estimator, which refits the non-zero parameters of the former estimator without penalty in the criterion function. We demonstrate via simulations that our method is not dominated by cross-validation in terms of estimation errors and outperforms cross-validation in terms of inference. As an illustration, we revisit Fryer Jr (2019), who investigated racial differences in police use of force, and confirm his findings.

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  • Denis Chetverikov & Jesper Riis-Vestergaard S{o}rensen, 2021. "Selecting Penalty Parameters of High-Dimensional M-Estimators using Bootstrapping after Cross-Validation," Papers 2104.04716, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2104.04716
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    References listed on IDEAS

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    Cited by:

    1. Yuehao Bai & Liang Jiang & Joseph P. Romano & Azeem M. Shaikh & Yichong Zhang, 2023. "Covariate Adjustment in Experiments with Matched Pairs," Papers 2302.04380, arXiv.org, revised Oct 2023.

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