Admissibility Of Linear Estimators In Linear Models With Respect To Inequality Constraints

On the basis of reference [25], the admissibility of linear estimators in linear models with respect to inequality constraints is investigated in this paper, which generalizes some known results in the past.The thesis is composed of five parts. In the first part, we make a brief review about the development in the theory of admissibility and some matrix introduction relates to this paper.In the second part, we study the linear model (Y, Xβ, V) with the inequality constraint RXβ ≥ 0, where V > 0 is known, the characterization for a linear estimator of β to be admissible in the class of all estimators is given, see Theorem 2.1-2.3.In part three and four, we explore the multivariate linear model (Y, XB, Σ(?) V) with the restriction tr(RB) ≥ 0 under quadratic loss function and matrix loss function respectively. In the third part, the necessary and sufficient conditions for LY (LY+L₁) to be admissible of SB among homogeneous (inhomogeneous) linear estimators are obtained, see Theorem 3.1-3.3. In the fourth part, we characterize the admissibility of AY in the class of homogeneous linear estimators, see Theorem 4.1. Meanwhile, a necessary and a sufficient condition for AY + A₁ to be admissible among inhomogeneous linear estimators are also presented, see Theorem 4.2 and 4.3.In the last part, we propose some meaningful questions to be solved.