Linear Ev Model

The content of this thesis is linear EV(errors-in-variables) regression models, that is regression models with measurement error. Because data are often obtained with measurement error in fact, EV model is more fit in application than the ordinary regression model. While it is more complicate in statistical inference and analysis, research about theory is very difficulty.The main results of this thesis are the following three parts.1. Problem about the existence of the unbiased estimator of regression parameters in the simple linear EV model is thoroughly solved. The non-existent of unbiased estimator under some common restrictions are proved. The condition that "reliability ratio is known" is generalized to an important case under which unbiased estimator exists, the sufficient and necessary condition for its existence and the formation of unbiased estimator are also put forward.2. The large sample properties of LS estimator in the linear EV model are discussed. The sufficient and necessary condition for the strong and weak consistency are proved to be the same, hence the strong and weak consistency for LS estimator are equivalent just as the ordinary linear regression model. Two conditions under which quadratic-mean consistency holds are given. A counter example shows that weak consistency and quadratic-mean consistency are non-equivalent and that the existence of arbitrary order moments cannot guarantee the quadratic-mean consistency.3. The linear EV model with replicated observations only on explanatory variables is studied. Estimators of parameters are given. The consistency and asymptotic normality of the given estimators are proved with the help of extension of Jamison Theorem.