Asymptotic Properties of Lasso Estimators

Abstract: We look into the behavior of the bootstrapped Lasso estimator and show that it is inconsistent. A modified bootstrap method is proposed and is shown to be consistent in estimating the distribution function, bias and variance of the Lasso estimator. As an application, a data based method of choosing the optimal penalty parameter is also discussed. Some preliminary asymptotic results for Lasso estimators in high dimensions will also be presented.