Bootstrapping Lasso-type Estimators Under Moving Parameter Framework
We study the distribution properties of Lasso-type regression estimators in a moving-parameter asymptotic framework and consider bootstrapping them accordingly. It has been proved that the distribution function of Lasso-type estimators including adaptive lasso and SCAD cannot be consistently estimated, especially when the underlying regression parameter is in a shrinking neighborhood of the origin. However, under certain criteria, we expect to show some bootstrap methods could be used to simulate Lasso-type estimators in most cases. A numerical simulation will also be provided to help visualize the non-normal nature of the distribution of Lasso-type estimators and help investigate the performance of the selected bootstrap methods.