Establishing Equalities of OLSEs and BLUEs Under Seemingly Unrelated Regression Models

Original Article


Seemingly unrelated regression models (SURMs) are extensions of linear regression models which allow correlated errors between regression equations. The purpose of this article is to reconsider some fundamental problems on the performance and connection of ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) of parametric functions under an SURM. Motivated by a variety of known results and facts on the equivalence of OLSEs and BLUEs under general linear models, this article collects a list of necessary and sufficient conditions for OLSEs to be BLUEs under an SURM and presents a variety of statistical interpretations on the equivalence of OLSEs and BLUEs under the SURM.


SURM OLSE BLUE Equivalence Statistical interpretation 

Mathematics Subject Classification

62F11 62H12 62J05 



The author wishes to thank two referees for their helpful comments and suggestions on this article.


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Copyright information

© Grace Scientific Publishing 2018

Authors and Affiliations

  1. 1.Fuxin Higher Training CollegeFuxinChina

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