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

Some admissibility of linear estimators in stochastic effective linear models with respect to inequality constraints are 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 ma-trix introduction relates to this paper.In the second part,we study the linear model (Y,Xβ,σ~2V)with the inequality constraint Rβ≮0,where V≥0 is known.Under matrix loss function,the necessary and sufficient conditon for estimators is admissible among inhomogeneous class are given.In part three and four,we explore the stochastic effective linear model(Y,Xβ,σ~2V)with the restriction RX Aα≥0andRXAα≮0in the theory of admissibility.Admissibility of both homogeneous and inhomogeneous linear estimators is investigated in stochastic effective linear models with respect to inequality constraints.The relation between admissibility of the two types of esti-mators is derived.In the third part,under quadratic loss function the necessary and sufficient conditions for(LY+a)to be admissible of Sα+Qβamong inhomogeneous linear estimators are obtained.In the fourth part,we characterize the admissibility in the class of inhomogeneous linear estimators under matrix loss function.In the last part,we propose some meaningful questions to be solved.