In this study, Professor Chih-Ling Tsai and co-authors Yiyun Zhang and Runze Li apply the nonconcave penalized likelihood approach to obtain variable selections as well as shrinkage estimators. This approach relies heavily on the choice of regularization parameter, which controls the model complexity.

In this paper, the authors propose employing the generalized information criterion, encompassing the commonly used Akaike information criterion (AIC) and Bayesian information criterion (BIC), for selecting the regularization parameter. Their proposal makes a connection between the classical variable selection criteria and the regularization parameter selections for the nonconcave penalized likelihood approaches. The authors show that the BIC-type selector enables identification of the true model consistently, and the resulting estimator possesses the oracle property in the terminology of Fan and Li (2001).