The Best Linear Unbiased Estimation And The Admissibility Of Estimators Of The Regression Coefficients Matrix Under Generalized Balanced Losses

For the generalized multivariate linear model: where Xnxp and Vnxn≥0 are known matrixes with rank(X)= p, whereasθ∈Rpxq is an unknown parameter matrix. And∑qXq≥0 is a non-zero matrix, it may be known or partly known. A new generalized loss function is defined by modifying the balanced loss function given by Zellner, called generalized balanced loss function: (Y-Xδ(Y))'U1(Y-Xδ(Y))+{δ(Y)-θ)'U2{δ(Y)-θ), whereδ(Y) is an estimator ofθ,ω€[0,1],U1≥0 and U2> 0 are known. For the generalized multivariate linear model, the goal of this paper is to study the best linear unbiased estimation and the admissibility of estimators of the regression coefficients matrix under the generalized balanced loss function.The organization of this paper is as follows:Chapter 1, the background of the research is given, main results of related issues are also included.Chapter 2 is devoted to give some basic knowledge related with the investigation of the article.Chapter 3 is devoted to introduce the balanced loss function under all kinds of the linear model, then the generalized balanced loss function is is given.Chapter 4 is devoted to study the best linear unbiased estimation of the regres-sion coefficients matrix under a generalized balanced loss function.In Chapter 5, the necessary and sufficient condition for a linear estimators of the regression coefficients matrix to be admissible under a generalized balanced loss function is obtained.