Analytic and bootstrap-after-cross-validation methods for selecting penalty parameters of highdimensional M-estimators - Denis N. éCetverikov; Jesper R-V Sørensen (Centre for Microdata Methods and Practice (cemmap), 2021)
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-aftercross-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.
Keywords: 330; Penalty parameter selection; penalized M-estimation; high-dimensional models; sparsity; cross-validation; bootstrap