Analytic and bootstrap-after-cross-validation methods for selecting penalty parameters of high-dimensional M-estimators - Denis N. Chetverikov; Jesper R.-V. Sørensen (Centre for Microdata Methods and Practice (cemmap), 2022)
We develop two new methods for selecting the penalty parameter for the e1-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 e1-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: 330; Penalty parameter selection; penalized M-estimation; high-dimensional models; sparsity; cross-validation; bootstrap