The Chord Method Of Parameter Estimation In The EV Model

Since Adocock first discussed the regression model with errors in both variables in 1877,the EV model has been paid more and more attention.In general linear models,we only think that linear models or dependent variables have errors,but we do not consider the measurement errors of independent variables.This leads to some inadequacies in linear statistical models in some cases.In many practical cases,Among the observed data,not only does the dependent variable have measurement error,but also the measurement of the independent variable.If the measurement error of the independent variable is not considered,it will lead to the deficiency of the simple linear statistical model in some practical problems,making the analysis result far from the actual.The errors-in-variables(EV)model is introduced to overcome such problems.Many of the properties of the EV model have been summarized in the literature [3].In the EV model,we usually study the problem of parameter estimation in the model.At present,the least squares method in the linear model,the generalized least squares method,the maximum likelihood estimation method and the moment estimation method are used.See Literature [4-10].However,these methods are not suitable for the EV model or some harsh conditions are attached.Therefore,in this paper,a new estimation method,the chord estimation method,is used to estimate the parameters in the EV model.The chord estimation method considers the measurement error of the independent variable and also considers the measurement error of the dependent variable.It has some similarities with the orthogonal estimation,but the essence is not the same,although the chord estimation method produces Chord estimators are sometimes not consistent estimators,they have obvious advantages in estimating the effect,especially when doing numerical simulations,the estimation effect is better,which is also an important reason for the study of string estimation in this paper.The literature [11] first proposed the orthogonal estimation method of parameters.The literature [12] studied the orthogonal estimator of the parameters in the linear EV model with constant coefficient and its properties.The literature [13-15] studied the orthogonal estimator of parameters and its properties in the variable coefficient EV model.The literature [16,17] used the adjusted least squares method to study the estimator and its properties in the variable coefficient EV model.Under these main references,this paper mainly studies the parameter estimates in the EV model and discusses the limit properties of these estimators.The structure of this paper is as follows:In the first chapter,this paper mainly introduces the background,significance of the topic and related symbols.In the second chapter,the chord estimators of parameters in the constant coefficient linear EV model are obtained under the condition that both independent and dependent variables have measurement errors,and analyzes the superiority of the estimator and the limit property of the chord estimator,and carries out numerical simulation.In chapter three,the chord estimator of parameters in variable coefficient linear EV model is obtained under the condition that both independent and dependent variables have measurement errors,and discusses the limit property of the estimator.Finally,the conclusion of this paper is a summary of the current research work and a prospect for future research directions.