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

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Abstract

We develop two new methods for selecting the penalty parameter for the `1-penalized high-dimensional M-estimator, which we refer to as the analytic and bootstrap-aftercross-validation methods. For both methods, we derive nonasymptotic error bounds for the corresponding `1-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.
Original languageEnglish
Number of pages63
Publication statusPublished - 10 Apr 2021
SeriesUniversity of Copenhagen. Institute of Economics. Discussion Papers (Online)
Number04
Volume21
ISSN1601-2461

Keywords

  • Faculty of Social Sciences
  • penalty parameter selection
  • penalized M-estimation
  • high-dimentional models
  • sparsity
  • cross-validation
  • bootstrap

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