Tuning Parameter Selection for the Adaptive Lasso using ERIC

10 The adaptive lasso is a commonly applied penalty for variable selection in regression mod11 eling. Like all penalties though, its performance depends critically on the choice of tuning 12 parameter. One method for choosing the tuning parameter is via information criteria, such as 13 those based on AIC and BIC. However, these criteria were developed for use with unpenal14 ized maximum likelihood estimators, and it is not clear that they take into account the effects 15 of penalization. In this article, we propose the Extended Regularized Information Criterion 16 (ERIC) for choosing the tuning parameter in adaptive lasso regression. ERIC extends the BIC 17 to account for the effect of applying the adaptive lasso on the bias-variance tradeoff. This leads 18 to a criterion whose penalty for model complexity is itself a function of the tuning parameter. 19 We show the tuning parameter chosen by ERIC is selection consistent when the number 20 of variables grows with sample size, and that this consistency holds in a wider range of con21 texts compared to using BIC to choose the tuning parameter. Simulation show that ERIC can 22 significantly outperform BIC and other information criteria proposed (for choosing the tuning 23 parameter) in selecting the true model. For ultra high-dimensional data (p > n), we consider 24 ∗Corresponding author: [email protected]; School of Mathematics and Statistics, The University of New South Wales, 2052, Sydney, Australia 1 ACCEPTED MANUSCRIPT D ow nl oa de d by [ U ni ve rs ity N or th C ar ol in a C ha pe l H ill ] at 0 7: 03 0 4 Se pt em be r 20 14