Estimation in singular linear models with stepwise inclusion of linear restrictions

摘要

In this paper, we consider the general linear model M = {y, X beta, Sigma), without any rank assumptions to the model matrix X and covariance matrix Sigma, and its two restricted models Mr(1) = {y, X beta vertical bar A(1)beta = r(1), Sigma} and Mr(12) = , {y,X beta vertical bar A beta = r, Sigma}, where r = (r(1)', r(2)')' and A = (A(1)', A(2)')'. We give the necessary and sufficient conditions for the BLUEs to equal under M and Mr(1), as well as under Mr(1) and Mr(12). We also derive that the BLUEs under Mr(1) are superior to the BLUEs under M, and that the BLUEs under Mr(12) are superior to the BLUEs under Mr(1) in the sense of the covariance matrix. (c) 2016 Elsevier Inc. All rights reserved.