Group variable selection via SCAD-L₂

Abstract

We propose a penalized regression method SCAD-L₂ using a penalty function called SCAD (smoothly clipped absolute deviation) combined with an L₂ penalty. The new method inherits good features of SCAD, namely unbiasedness, continuity, and sparsity. In addition, it favours another important property that highly correlated variables are in or out a model together. SCAD-L₂ derives its power by focusing on group variable selection. For data with dependent structures, where traditional variable selection methods are unstable, SCAD-L₂ can select variable groups and preserve small prediction errors.

Keywords:

• elastic net
• Lasso
• oracle property
• SCAD
• variable selection

Acknowledgements

This work was supported by National Science Foundation Grant DMS-0604776. The authors thank the editor and the anonymous referee for their comments and suggestions that improved the paper.