Exponential Squared Loss-Based Robust Variable Selection with Prior Information in Linear Regression Models

This paper proposes a robust variable selection method that incorporates prior information through linear constraints. For more than a decade, penalized likelihood frameworks have been the predominant approach for variable selection, where appropriate loss and penalty functions are selected to formulate unconstrained optimization problems. However, in many specific applications, some prior information can be obtained. In this paper, we reformulate variable selection by incorporating prior knowledge as linear constraints. In addition, the loss function adopted in this paper is a robust exponential squared loss function, which ensures that the estimation of model parameter coefficient will not have a great impact when there are a few outliers in the dataset. This paper uses the designed solution algorithm to calculate the estimated values of coefficients and some other parameters, and finally conducts numerical simulations and a real-data experiment. Experimental results demonstrate that our model significantly improves estimation robustness compared to existing methods, even in outlier-contaminated scenarios.