Research On Estimation Methods Of Nonlinear Regression Models With Measurement Errors

Measurement error models originated early and have been widely used in life,such as biology,economics and engineering.This is mainly because when people observe variables,there are often various deviations.If we neglect the deviation and then use the conventional estimation method to estimate,it will cause the bias and inconsistency of parameter estimation in the model.Because of the limitation of linear regression models,nonlinear regression models are more suitable for many practical problems.Therefore,this paper adds measurement errors to nonlinear regression models and studies their estimation methods.Firstly,this paper introduces some common estimation methods of classical linear regression models with measurement errors.Then,on the basis of these estimation methods,focusing on the estimation methods of nonlinear regression models with measurement errors.For quadratic generalized linear models,which are special nonlinear regression models,the parameter estimators and their asymptotic properties of quadratic generalized linear models with measurement errors are given,and the extensively corrected score method is improved.Compared with the conventional corrected score method,the weighted corrected score method and the extensively corrected score method,this method eliminates some of their limitations.For general nonlinear regression models with measurement errors,two estimation methods are given in this paper.The first method is to transform nonlinear regression models into linear regression models by using the kernel function theory in machine learning,and then use the least squares method to do regression.During the period,the influence of measurement errors is corrected by using factor scores method.The second method is similar to the first,which combines support vector regression and factor scores method,but its solution is sparse compared with the first method.The latter two methods are unified in form and have low requirements for the form of models and the distribution of measurement errors.Then,numerical simulation is carried out by using R software,and better simulation results can be obtained by comparing with conventional estimation methods which neglect measurement errors.Finally,an example is given to analyze the operation data of a combined cycle power plant in order to predict the net electrical energy output of the power plant,and to compare with the conventional estimation method which neglects measurement errors.