Variable selection for uncertain regression models based on elastic net method

On one hand, determining the exact number of explanatory variables in uncertain regression analysis is often challenging, as real-world scenarios are interconnected. On the other hand, it's worth noting that even when the number of variables is determined, some variables may have minimal impact on the response variable, and retaining them would only increase the complexity of the model. Therefore, variable selection methods can help eliminate variables with minimal impact to enhance the simplicity and interpretability of the model. In light of this, this paper first introduces a novel variable selection strategy based on the elastic net method to address the variable selection problem in uncertain regression models. This method not only offers the flexibility to simplify uncertain regression analysis into Lasso estimation or Ridge estimation but also exhibits extremely high efficiency in variable selection. Secondly, to address the issue of determining tuning parameters, we introduce the cross-validation method to ensure optimal model performance. Furthermore, we propose an uncertain hypothesis testing method based on imprecise observational data, which can help us assess the suitability of estimated parameters. Finally, through a series of numerical examples, we validate the feasibility and effectiveness of this method.