Research On Restriction Estimation In Linear Regression Model And Linear Measurement Error Model And Their Properties

The linear models play a central part in modern statistical methods and have bec- ome the most widely used models in modern statistics. In this paper, we mainly focus on the properties of parametrical estimation under Pitman's closeness criterion in linear model and the consistent estimators and their properties in linear measurement error model when prior information is given in the form of exact or stochastic linear rest- rictions.The performances of the r-k class estimator and the r-d class estimator relative to the least squares estimator are considered in this thesis. This paper develops the Pitman mea sure of closeness of those estimators relative to the ordinary least squares estima- tion under a balanced loss function and multivariate normal distribution error terms, and its approximation is computed by Monte Carlo simulation. Furthermore, it is shown theoretically that Theil's mixed regression estimator dominates the ordinary least squa- res under Pitman closeness criterion almost surely.In chapter four and five we consider the linear measurement error models. Several consistent estimators satisfying exact linear restrictions are proposed when either the co- variance matrix of measurement errors or the reliability matrix is known. Their asymp- totic distributions are obtained with not necessarily normally distributed measurement errors. It is shown that making use of the exact linear restrictions improves the effici- ency of the estimators in measurement errors theoretically. A simulation study is carried out to illustrate the finite sample properties of the proposed estimators.The consistent estimators of the parameters in a linear measurement error model are discussed when stochastic linear restrictions on regression coefficients is available. We propose some methodologies to obtain the consistent estimation when either the cova- riance matrix of the measurement errors or reliability matrix with independent variables is known. The exact distributions of these estimators is hard to obtain. Evev if obtained, it is very difficult to draw statistical inferences because of its complicated expressions. when the sample size is large, these estimators have the same asymptotic distribution. A Monte Carlo simulation is carried out to study the the finite properties of the estimators.