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

Author

Listed:
  • Denis Chetverikov

    (Department of Economics, UCLA)

  • Jesper R.-V. Sørensen

    (Department of Economics, University of Copenhagen)

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.

Suggested Citation

  • Denis Chetverikov & Jesper R.-V. Sørensen, 2021. "Analytic and Bootstrap-after-Cross-Validation Methods for Selecting Penalty Parameters of High-Dimensional M-Estimators," Discussion Papers 21-04, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:2104
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    References listed on IDEAS

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    3. Adam Baybutt & Manu Navjeevan, 2023. "Doubly-Robust Inference for Conditional Average Treatment Effects with High-Dimensional Controls," Papers 2301.06283, arXiv.org.

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