Adaptive bridge regression modeling with model selection criteria

We consider the problem of constructing an adaptive bridge regression modeling, which is a penalized procedure by imposing different weights to different coefficients in the bridge penalty term. A crucial issue in the modeling process is the choices of adjusted parameters included in the models. We treat the selection of the adjusted parameters as model selection and evaluation problems. In order to select the parameters, model selection criteria are derived from information-theoretic and Bayesian approach. We conduct some numerical studies to investigate the effectiveness of our proposed modeling strategy.