Analytic and Bootstrap-after-Cross-Validation Methods for Selecting Penalty Parameters of High-Dimensional M-Estimators
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We develop two new methods for selecting the penalty parameter for the ℓ^1-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 ℓ^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.
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