Selecting Penalty Parameters of High-Dimensional M-Estimators using Bootstrapping after Cross-Validation
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866912116463632384 |
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| author | Chetverikov, Denis Sørensen, Jesper Riis-Vestergaard |
| author_facet | Chetverikov, Denis Sørensen, Jesper Riis-Vestergaard |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2104_04716 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Selecting Penalty Parameters of High-Dimensional M-Estimators using Bootstrapping after Cross-Validation Chetverikov, Denis Sørensen, Jesper Riis-Vestergaard Statistics Theory Econometrics 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. |
| title | Selecting Penalty Parameters of High-Dimensional M-Estimators using Bootstrapping after Cross-Validation |
| topic | Statistics Theory Econometrics |
| url | https://arxiv.org/abs/2104.04716 |