Some Decompositions of OLSEs and BLUEs Under a Partitioned Linear Model |
| |
Authors: | Yongge Tian |
| |
Affiliation: | School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China E-mail: |
| |
Abstract: | We consider in this paper a partitioned linear model { y , X 1 β 1 + X 2 β 2 , σ 2 σ } and two corresponding small models { y , X 1 β 1 , σ 2 σ } and { y , X 2 β 2 , σ 2 σ } . We derive necessary and sufficient conditions for (i) the ordinary least squares estimator under the full model to be the sum of the ordinary least squares estimators under the two small models; (ii) the best linear unbiased estimator under the full model to be the sum of the best linear unbiased estimators under the two small models; (iii) the best linear unbiased estimator under the full model to be the sum of the ordinary least squares estimators under the two small models. The proofs of the main results in this paper also demonstrate how to use the matrix rank method for characterizing various equalities of estimators under general linear models. |
| |
Keywords: | Partitioned linear model small model ordinary least squares estimator (OLSE) best linear unbiased estimator (BLUE) decomposition of estimator rank formulas for partitioned matrices elementary block matrix operations (EBMOs) |
|
|