Analytic and Bootstrap-after-Cross-Validation Methods for Selecting Penalty Parameters of High-Dimensional M-Estimators

Denis Chetverikov and Jesper R.-V. Sørensen
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Denis Chetverikov: Department of Economics, UCLA
Jesper R.-V. Sørensen: Department of Economics, University of Copenhagen

No 21-04, Discussion Papers from University of Copenhagen. Department of Economics

Abstract: We develop two new methods for selecting the penalty parameter for the L1-penalized high-dimensional M-estimator, which we refer to as the analytic and bootstrap-after-cross-validation methods. For both methods, we derive nonasymptotic error bounds for the corresponding L1-penalized M-estimator and show that the bounds converge to zero under mild conditions, thus providing a theoretical justification for these methods. We demonstrate via simulations that the finite-sample performance of our methods is much better than that of previously available and theoretically justified methods.

Keywords: penalty parameter selection; penalized M-estimation; high-dimensional models; sparsity; cross-validation; bootstrap (search for similar items in EconPapers)
Date: 2021-05-05
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Citations: View citations in EconPapers (2)

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