Simultaneous estimation and variable selection in median regression using Lasso-type penalty

Abstract

We consider the median regression with a LASSO-type penalty term for variable selection. With the fixed number of variables in regression model, a twostage method is proposed for simultaneous estimation and variable selection where the degree of penalty is adaptively chosen. A Bayesian information criterion type approach is proposed and used to obtain a data-driven procedure which is proved to automatically select asymptotically optimal tuning parameters. It is shown that the resultant estimator achieves the so-called oracle property. The combination of the median regression and LASSO penalty is computationally easy to implement via the standard linear programming.Arandom perturbation scheme can be made use of to get simple estimator of the standard error. Simulation studies are conducted to assess the finite-sample performance of the proposed method.We illustrate the methodology with a real example.© The Institute of Statistical Mathematics, Tokyo 2008.