Estimation Of Parameters And Statistical Properties In The Error-in-Variable Models

Linear models have rich theory and widespread useness in modern statistics. Error-in-Variable models are promotion of general linear models. Their theoretical researches have attracted more and more attention and people have scored many important results.In this paper, we consider Error-in-Variable models: Where c and a are parameters andεi is random error. The parameter theories of Error-in-Variable models are researched systematically and the excellent statistical properties of estimable function xa are discussed.There are five chapters in this paper. In chapter 1, many parameter estimation theories of linear models are introduced and we also discuss prepared knowledge which include least square estimate, generalized inverse, relative eigenvalue etc. In chapter 2, we discuss estimation methods of parameters in the Error-in-Variable modelsand the least square estimate and generalized least square estimate are given. In chapter 3, we study some statistical properties of estimable function xa in Error-in-Variable models. They include on robustness in terms of error distributions, Pitman superiority etc. The largest distribution category are given to maintain the good statistical of the least square estimate and generalized least square estimate. The conclusion is got that the generalized least square estimate is better than the least square estimate according to Pitman nearness. In chapter 4, we discuss the non-linear Error-in-Variable models and give a robust estimate. In chapter 5, based on a volume model, the parameter estimation of general models and Error-in-Variable models are given by means of stochastic simulation method. We compare the two different estimation methods and get a conclusion that the estimate of Error-in-Variable models is better than the estimate of general model when the variables contain measurement error which we should not overlook.