Exponential Squared Loss-Based Robust Variable Selection with Prior Information in Linear Regression Models
Year: 2025
Type: article
Abstract: 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.
Source: Axioms
Authors: Hejun Wei, Tian Jin, Yunquan Song
Institution: China University of Petroleum, East China
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
Award: G48183633
OpenAlex ID: W4412083249