Improvement Of Parameter Estimation Strategy For A Class Of Differential Equations

Differential equation model is widely used in many fields of science,and its qualitative and quantitative research is a hot topic in the field of mathematics and statistics.Based on the recognition of the structure of the equation model,the parameter estimation of the model is the focus of modeling research.In this paper,the parameter estimation of differential equation model is studied,and the two-step estimation strategy proposed by Liang and Wu is improved.Firstly,the Liang and Wu's estimation strategy is studied numerically in this paper.Because the local polynomial estimation method is adopted in the first step of the method,aiming at the influence of the selection of kernel function and window width on the whole estimation strategy,this paper compares the effects of different kernel functions and window widths on the effectiveness of the method by numerical analysis and comparison of the influence of different kernel functions and window widths on the effectiveness of the method.It is pointed out that the selection of kernel function has little effect on the estimation strategy,and the window width has a great influence on the estimation strategy.In practical application,the appropriate window width should be selected according to the data.Then,the method of Liang and Wu's is improved,the linearization method is adopted in the second step of the estimation strategy,thus the explicit expression of the parameter estimation is obtained and the consistency of the estimation is proved.Finally,the simulation results of practical model show the effectiveness of the proposed method.On the basis of the simplified algorithm,the proposed method has no loss of estimation accuracy.