A new type of generalized information criterion for regularization parameter selection in penalized regression with application to treatment process data

Abstract

ABSTRACT We propose a new approach to select the regularization parameter using a new version of the generalized information criterion ( GIC ) in the subject of penalized regression. We prove the identifiability of bridge regression model as a prerequisite of statistical modeling. Then, we propose asymptotically efficient generalized information criterion ( AGIC ) and prove that it has asymptotic loss efficiency. Also, we verified the better performance of AGIC in comparison to the older versions of GIC . Furthermore, we propose MSE search paths to order the selected features by lasso regression based on numerical studies. The MSE search paths provide a way to cover the lack of feature ordering in lasso regression model. The performance of AGIC with other types of GIC is compared using MSE and model utility in simulation study. We exert AGIC and other criteria to analyze breast and prostate cancer and Parkinson disease datasets. The results confirm the superiority of AGIC in almost all situations.