Shared Concepts

This section applies to the REGSELECT procedure.

Adaptive elastic net selection (Zou and Zhang 2009) is an improved version of the elastic net and adaptive LASSO selection methods. Adaptive elastic net penalizes the squared error loss by using a combination of the penalty and the adaptive penalty.

More specifically, the adaptive elastic net coefficients are the solution to the optimization problem

The adaptively weighted penalty achieves the oracle property, and the elastic net penalty handles the collinearity. The adaptive weights can be obtained by ridge regression estimation.

Like the naive elastic net, the adaptive elastic net can be transformed into an adaptive LASSO-type problem in some augmented space

where the augmented design matrix and response are defined by