Mixed smoothly clipped absolute deviation estimator for stochastic restricted regression models

As datasets and features continue to grow, selecting appropriate variables to ensure the efficiency and accuracy of models becomes critical. The smoothly clipped absolute deviation (SCAD) method possesses the oracle property and combines the advantages of the optimal subset and Lasso with good sparsity, while simultaneously guaranteeing continuity with no bias. However, these methods are not suitable for handling data under stochastic restrictions. The mixed-Lasso (M-Lasso) method introduces stochastic restrictions into the model to obtain additional information; however, the solution to this method is not sufficiently stable and is sensitive to the selection of parameters. In this study, a mixed SCAD method is proposed, which is an extension of SCAD that considers stochastic restrictions. This method further improves the accuracy of the model prediction and has higher stability and effectiveness than M-Lasso. The stability and effectiveness of the method are verified through simulation experiments and real data. In the prostate dataset and riboflavin dataset, the Bayesian information criterion value of the proposed method was found to be 1.1561 (∼4%) less than that of M-Lasso.