Adaptive Monte Carlo method for nonlinear mixed additive and multiplicative errors model

Abstract In order to assess the precision of the parameter estimation of the nonlinear mixed additive and multiplicative errors model, there is a complicated derivative problem. This paper firstly derives the precision assessment formula of the existing solution method of the model based on the approximate function expression method, and then introduces the Monte Carlo method in the probability distribution method of the approximate function to assess the precision of the parameter estimation results of the model, which can avoid the complicated derivative operation. Meanwhile, in response to the low computational efficiency of the Monte Carlo method and the blindness in the selection of the number of simulations, an adaptive Monte Carlo method with relatively stable results is derived by using a given numerical tolerance to obtain the required number of simulations. Finally, through the analysis of the results of the example, it can be concluded that the adaptive Monte Carlo method has wider applicability and potential application prospects.