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 -