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

Denis Chetverikov, Jesper Riis-Vestergaard Sørensen

arXiv 10 Apr 2021 · Mathematics — Statistics Theory · publishedJournal of Political Economy (2025) · 3 citations (OpenAlex)

arXiv:2104.04716 · PDF · DOI · OpenAlex · Extracted main text

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 entries of the former estimator without penalty in the criterion function. We demonstrate via simulations that our methods are not dominated by cross-validation in terms of estimation errors and can outperform cross-validation in terms of inference. As an empirical illustration, we revisit Fryer Jr (2019), who investigated racial differences in police use of force, and confirm his findings.

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61
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Fryer Jr, R. G (2019) An empirical analysis of racial differences in police use of force1.000123100%
2Negahban, S. N., P. Ravikumar, M. J. Wainwright, and B. Yu (2012) A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers0.9568488%
3van de Geer, S. A (2008) High-Dimensional Generalized Linear Models and the Lasso0.8947371%
4Wainwright, M. J (2019) High-dimensional statistics: A non-asymptotic viewpoint0.84333100%
5Belloni, A. and V. Chernozhukov (2011) a): $_1$-penalized quantile regression in high-dimensional sparse models0.81142100%
6Belloni, A., V. Chernozhukov, and Y. Wei (2016) Post-selection inference for generalized linear models with many controls0.73710340%
7Honoré, B. E (1992) Trimmed LAD and least squares estimation of truncated and censored regression models with fixed effects0.73732100%
8Belloni, A., V. Chernozhukov, D. Chetverikov, C. Hansen, and K. Kato (2018) a): High-dimensional econometrics and regularized GMM0.69312333%
9Bickel, P. J., Y. Ritov, and A. B. Tsybakov (2009) Simultaneous analysis of Lasso and Dantzig selector0.6444250%
10Chernozhukov, V., D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W… (2018) Double/debiased machine learning for treatment and structural parameters0.64422100%

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