Sparse and robust estimation with ridge minimax concave penalty

Feature selection is an important procedure that is used in data mining to extract valuable information from large quantities of data. Existing penalization methods use a single penalty function to select important features. However, these methods do not yield sufficiently accurate predictions and selection outcomes. Therefore, construction of a concise and efficient prediction model would be beneficial. In this study, we propose a novel penalty function using a ridge and minimax concave penalty to overcome the limitations of individual penalty functions. Furthermore, we introduce a robust penalized feature selection method with Huber loss function, which is implemented by a local approximation algorithm. The theoretical properties of the algorithm have been described. Simulated and real-world data analyses are used to demonstrate the efficacy of the proposed method.