title: 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 two-stage 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. A random 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.
authors: Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546, Singapore.
authors: Jinfeng
authors: J
authors: Xu
authors: Zhiliang
authors: Z
authors: Ying
keywords: Bayesian information criterion; Lasso; Least absolute deviations; Median regression; Perturbation; Variable selection
references: J Urol. 1989 May;141(5):1076-83
references: 2468795