Admissibility And General Admissibility Of Estimators In Linear Models With Respect To Several Constraints

In this paper, the admissibility and general admissibility of linear estimators in general multivariate growth curve model with respect to constraints among homogeneous linear estimators and non-homogeneous linear estimators are considered. A lot of theoretical results are obtained. This total is divided into five parts. In the summary section, a simple linear model gives estimates to allow the development of history and the development of the situation at home and abroad, and gives the overview section of this paper is to be the main research In the first chapter, a simple review about the basic matrix knowledge of linear model is given ,and the admissibility and general admissibility of the linear function model 2(Y_i,A₀,A₁X,σ_i²Î£(?)V)with incomplete ellipsoid constraints X'A'₁'NA₁X≤σ_i²Î£(?) is also known. In the second chapter, we study the growth curve model X'A'₁'NA₁X≤σ_i²Î£(?) with respect to the constraints X'A'₁'NA₁X≤σ_i²Î£(?), the necessary and sufficient conditions of linear estimators of regression coefficients SXT in the class of homogeneous linear estimators and non-homogeneous linear estimators are gained,under the matrix loss function see some theorem 2.2.1-2.2.2. In the third chapter, under the quadratic loss function, we characterize the admissibility of of homogeneous linear estimators about multivariate growth curve model with respect to the same incomplete ellipsoidal constraints and the dual constraints BX = C, see theorem 3.1.1-3.1.3; and finally in the fourth chapter, the necessary and sufficient conditions of linear estimators of regression coefficients and parameters in multivariate linear model with inequality constrained trRi′A2Θ≥0, see theorem 4.1.1-4.1.3.Also the same to multivariate linear model with equality constrained NA2Θ= 0,see theorem 4.2.1-4.2.1.