Journal of Political Economy Vol. 133 No. 10 2025
Selecting Penalty Parameters of High-Dimensional M-Estimators Using Bootstrapping after Cross Validation
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.
- DOI
- 10.1086/736770
- Volume
- 133
- Issue
- 10
- Pages
- 3208-3248
- Language
- en
- Sources
- bibtex:phds-export.bib crossref openalex