TY - UNPB
T1 - Analytic and Bootstrap-after-Cross-Validation Methods for Selecting Penalty Parameters of High-Dimensional M-Estimators
AU - Chetverikov, Denis
AU - Sørensen, Jesper Riis-Vestergaard
PY - 2021/4/10
Y1 - 2021/4/10
N2 - We develop two new methods for selecting the penalty parameter for the `1-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 `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.
AB - We develop two new methods for selecting the penalty parameter for the `1-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 `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.
KW - Faculty of Social Sciences
KW - penalty parameter selection
KW - penalized M-estimation
KW - high-dimentional models
KW - sparsity
KW - cross-validation
KW - bootstrap
M3 - Working paper
T3 - University of Copenhagen. Institute of Economics. Discussion Papers (Online)
BT - Analytic and Bootstrap-after-Cross-Validation Methods for Selecting Penalty Parameters of High-Dimensional M-Estimators
ER -