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

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