Minimum relative error estimation for uncertain regression model with imprecise observations

In regression analysis, the least absolute deviation estimation is the most commonly used parameter estimation method in the presence of outliers, and it yields robust estimates by minimizing absolute errors. In practice, experts pay more attention to the relative error because it can intuitively demonstrate the relationship between predicted values and true values, and it is more robust to outliers. Based on the concepts of least absolute deviation estimation and relative error, this paper proposes an estimation method aimed at minimizing the relative error and applies it to uncertain regression models. The minimum relative error estimation method can efficiently capture the changing dynamics of the error in the given data, and then construct a more reasonable and reliable regression model in practical applications. In addition, this paper verifies the feasibility of the minimum relative error estimation method by giving specific numerical examples and compares it with the least absolute deviation estimation to show that the minimum relative error estimation has better fitting performance and robustness, especially in the presence of outliers.