Improved Estimation Of Parameters For Mixed-Effect Coefficient Linear Model And For Restricted Linear Regression Model

In this dissertation, some researches on improved estimation of parameters for Mixed-Effect Coefficient Linear Model and for a Linear Regression Model when additional linear restrictions of the parameter vector are assumed to hold. Local root estimator and Ridge estimator for Mixed-Effect Coefficient Linear Model and Restricted Stein-Rule estimator and its improved estimator are introduced. Is is organized as follows:Local Root estimator for Mixed-Effect Coefficient Linear Model is introduced in Chapter 2. The superiority of new estimator over the LSE under MSE is proved. Some properties, such as admissibility, efficiency and anti-interference are discussed.In Chapter 3, a Ridge estimator for Mixed-Effect Coefficient Linear Model is introduced. We prove the new estimator dominant LSE under MSE and discuss its admissibility.In Chapter 4, we introduce a Stein-Rule estimator for the vector of parameter in a linear regression model when additional linear restrictions of the parameter vector are assumed to hold. The estimator is a generalization of the well-known restricted LSE and is confined to the (affine) sub-space which is generated by the restrictions. Necessary and sufficient conditions for the superiority of the new estimator over the restricted LSE are derived.Improved estimation for Restricted Stein-Rule estimator is discussed in Chapter 5. Necessary and sufficient conditions for the superiority of the new estimator over the restricted LSE are derived. The new estimator is derived by minimuming MSE.