Selection of tuning parameters in bridge regression models via Bayesian information criterion

We consider bridge regression models, which can produce a sparse or non-sparse model by controlling a tuning parameter in the penalty term. A crucial part of a model building strategy is the selection of the values for adjusted parameters, such as regularization and tuning parameters. Indeed, this can be viewed as a problem in selecting and evaluating the model. We propose a Bayesian selection criterion for evaluating bridge regression models. This criterion enables us to objectively select the values of the adjusted parameters. We investigate the effectiveness of our proposed modeling strategy with some numerical examples.