Parameter Estimation of General Uncertain Differential Equations via the Principle of Least Squares with Its Application in Economic Field

The parameter estimation problem is one of the research hotspots in the field of uncertain differential equations. However, most studies at present focus on parameter estimation based on residuals of uncertain differential equations, which relies strictly on the solvability of residuals. In view of this disadvantage, this paper derives a symmetrical statistical invariant, which is different from residuals based on the difference scheme, and proposes the least squares estimation of general uncertain differential equations based on the statistical invariant and the principle of least squares. In order to consider parameter estimation in more general cases, this paper also studies the least squares estimation of time-varying parameters in general uncertain differential equations and designs corresponding to numerical algorithms to calculate the numerical solutions of these least squares estimations. Finally, this paper also proposes two numerical examples and an empirical study to illustrate the above methods.