Estimations of Parametric Functions under a System of Linear Regression Equations with Correlated Errors  

作　　者：Yong Ge TIAN 

机构地区：[1]China Economics and Management Academy, Central University of Finance and Economics, Beijing 100081, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第10期1927-1942,共16页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 70871073)

摘　　要：Estimations of parametric functions under a system of linear regression equations with correlated errors across equations involve many complicated operations of matrices and their generalized inverses. In the past several years, a useful tool -- the matrix rank method was utilized to simplify various complicated operations of matrices and their generalized inverses. In this paper, we use the matrix rank method to derive a variety of new algebraic and statistical properties for the best linear unbiased estimators （BLUEs） of parametric functions under the system. In particular, we give the necessary and sufficient conditions for some equalities, additive and block decompositions of BLUEs of parametric functions under the system to hold.Estimations of parametric functions under a system of linear regression equations with correlated errors across equations involve many complicated operations of matrices and their generalized inverses. In the past several years, a useful tool -- the matrix rank method was utilized to simplify various complicated operations of matrices and their generalized inverses. In this paper, we use the matrix rank method to derive a variety of new algebraic and statistical properties for the best linear unbiased estimators （BLUEs） of parametric functions under the system. In particular, we give the necessary and sufficient conditions for some equalities, additive and block decompositions of BLUEs of parametric functions under the system to hold.

关 键 词：Linear regression equations SUR model parametric functions ESTIMABILITY BLUE equalities of estimators decompositions of estimators matrix rank method 

分 类 号：O212.1[理学—概率论与数理统计] TG751[理学—数学]