Bootstrapping LASSO-type estimators in regression models

We study the consistency of the standard (non-parametric) bootstrap, the m-out-of-n bootstrap, and the oracle bootstrap distributions of some popular LASSO-type estimators in regression models with random predictors. These estimators have an oracle property and are often used in estimation of sparse regression models. A local asymptotic analysis further reveals the behavior of these estimators and of their bootstrap distributions when some regression coefficients approach zero at various rates. In a simulation study, we assess the finite sample properties of the estimators and of their bootstrap distributions for various sample sizes and model parameters. The analysis of a prostate cancer data set shows an application of LASSO-type inference and bootstrap methods in practice.