Group variable selection via SCAD-<i>L</i>₂

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.