Weighted Moment Estimation for Uncertain Delay Differential Equations and Its Application in Birth Rate Modeling

Uncertain delay differential equations can simultaneously describe uncertain disturbances and time-delay effects during the evolution process of a system, and parameter estimation is a crucial step in the application of uncertain delay differential equations. To address the issue of equal-weight imbalance in residual-based moment estimation, this paper investigates a weighted moment estimation method for uncertain delay differential equations based on uncertain theory. Specifically, a counterexample is presented to illustrate the equal-weight imbalance problem in the existing residual-based moment estimation, and a weighted moment estimation approach for uncertain delay differential equations is derived based on the idea of relative deviation. Subsequently, a numerical algorithm for calculating the weighted moment estimation is designed, and an empirical study modeling population birth rates is also provided to demonstrate the effectiveness of the method and numerical algorithm proposed in this paper.