an:05808522
Zbl 1197.62020
Tian, Yongge
On equalities of estimations of parametric functions under a general linear model and its restricted models
EN
Metrika 72, No. 3, 313-330 (2010).
00268516
2010
j
62F10 62J05 15A09 62F30
restricted linear model; OLSE; BLUE; parametric functions; estimability; equality of estimations
Summary: Estimations of parametric functions under a general linear model and its restricted models involve some complicated operations of matrices and their generalized inverses. In the past several years, a powerful tool, the matrix rank method was utilized to manipulate various complicated matrix expressions that involve generalized inverses of matrices. We use this method to derive necessary and sufficient conditions for six equalities of the ordinary least-squares estimators and the best linear unbiased estimators of parametric functions to equal under a general linear model and its corresponding restricted model.