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

81 Pages Posted: 13 May 2021 Last revised: 12 Jan 2022

See all articles by Jesper R.-V. Sørensen

Jesper R.-V. Sørensen

University of Copenhagen

Denis Chetverikov

University of California, Los Angeles (UCLA) - Department of Economics

Date Written: January 11, 2022

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,

Suggested Citation

Sørensen, Jesper Riis-Vestergaard and Chetverikov, Denis, Analytic and Bootstrap-after-Cross-Validation Methods for Selecting Penalty Parameters of High-Dimensional M-Estimators (January 11, 2022). Available at SSRN: https://ssrn.com/abstract=3844536 or http://dx.doi.org/10.2139/ssrn.3844536

Jesper Riis-Vestergaard Sørensen (Contact Author)

University of Copenhagen ( email )

Øster Farimagsgade 5, Bygn 26
Copenhagen, 1353
Denmark

HOME PAGE: http://https://sites.google.com/site/jesperrvs

Denis Chetverikov

University of California, Los Angeles (UCLA) - Department of Economics ( email )

8283 Bunche Hall
Los Angeles, CA 90095-1477
United States

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