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.
Analytic and bootstrap-after-cross-validation methods for selecting penalty parameters of high-dimensional M-estimators
20 April 2021
Working Paper (CWP20/21)