Least Absolute Deviation Estimation for Uncertain Regression Model via Uncertainty Distribution and Its Application in Sport Statistics

Uncertain regression analysis is a powerful tool for analyzing and interpreting the complex relationships between explanatory and response variables under uncertain environments, and a crucial step in analyzing datasets containing complex uncertainties is statistical inference based on uncertain parameter estimation methods. However, the existing parameter estimation studies of uncertain regression models all fail to effectively avoid the negative impact of outliers on the estimation results. To solve the above problem and further enrich the parameter estimation research, this paper constructs a symmetric statistical invariant for the uncertain regression model based on observed data and uncertain disturbance terms. Based on this statistical invariant, the least absolute deviation criterion is applied to propose a least absolute deviation estimation for the uncertain regression model. Finally, two numerical examples are provided to illustrate the advantages of the proposed method compared to existing methods, and the comparative results show that in certain scenarios, the least absolute deviation estimation method exhibits superior performance compared to other existing methods in terms of mean squared error, mean absolute error, and mean absolute percentage error. Furthermore, as a byproduct of this paper, the proposed method is applied to sports statistics, and two empirical cases are also provided to demonstrate the effectiveness of this application.