Universität Bonn

Department of Economics

Jesper Riis-Vestergaard Sørensen - University of Copenhagen

"Selecting Penalty Parameters of High-Dimensional M-Estimators using Bootstrapping after Cross-Validation", with Denis Chetverikov

Abstract

We develop a new method for selecting the penalty parameter for ℓ1-penalized M-estimators in high dimensions, which we refer to as bootstrapping after cross-validation. We derive rates of convergence for the corresponding ℓ1-penalized M-estimator and also for the post-ℓ1-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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