Nonparametric estimation of uncertain differential equations based on Laguerre polynomials

There has been a great deal of progress in the research on parameter estimation for uncertain differential equations (UDEs). However, in the modeling process, sometimes the amount of information obtained is not sufficient to construct a parametric model. For UDEs with nonparametric functions, this paper proposes a method based on Laguerre polynomials to convert nonparametric functions into parametric functions with weights. Estimates of the weights are derived with the help of the goodness of fit properties of the residuals, and the reasonableness is verified using uncertain hypothesis testing. Then two numerical examples are given to verify the feasibility of the proposed method. Finally, the proposed methodology is applied to the actual modeling of carbon dioxide emissions in China.