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

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