Residual-Based Improved Uncertain Maximum Likelihood Estimation for Uncertain Delay Differential Equations

As a powerful tool for characterizing the time-evolution behavior of dynamic systems with delay characteristics, the parameter estimation problem for uncertain delay differential equations has always been a research hotspot in the field of uncertain statistics. In order to eliminate the impact of outliers on the relevant results during parameter estimation, this paper proposes the improved uncertain maximum likelihood estimation and the generalized improved uncertain maximum likelihood estimation for uncertain delay differential equations based on symmetric statistical invariants, named residuals. After that, a numerical algorithm is also designed to solve the numerical solutions of the corresponding estimators. Finally, two numerical examples and an empirical study on stock price modeling are provided to illustrate the effectiveness of the methods proposed in this paper.