Tuning Parameter Selection for the Adaptive Lasso Using ERIC

This leads to a criterion whose penalty for model complexity is itself a function of the tuning parameter. We show the tuning parameter chosen by ERIC is selection consistent when the number of variables grows with sample size, and that this consistency holds in a wider range of contexts compared to using BIC to choose the tuning parameter. Simulation show that ERIC can significantly outperform BIC and other information criteria proposed (for choosing the tuning parameter) in selecting the true model.

For ultra high-dimensional data ( p > n ), we consider a two-stage approach combining sure independence screening with adaptive Lasso regression using ERIC, which is selection consistent and performs strongly in simulation. Supplementary materials for this article are available online.