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Statistical Papers

, Volume 60, Issue 1, pp 273–292 | Cite as

On the equality of estimators under a general partitioned linear model with parameter restrictions

  • Bo JiangEmail author
  • Yuqin Sun
Regular Article

Abstract

Assume that a linear regression model is written as a partitioned form. In such a case, it is quite convenient to determine the role of each subset of regressors, and to derive estimators of unknown partial parameters in the partitioned model. In this paper, we consider the relationships between the well-known ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) of the whole and partial mean parameter vectors in a general partitioned linear model with parameter restrictions. We first review some known results on the OLSEs and the BLUEs and their properties under general linear models. We then present a variety of necessary and sufficient conditions for OLSEs to be BLUEs under a general partitioned linear model with parameter restrictions.

Keywords

Partitioned linear model Parametric functions Estimability OLSE BLUE Estimator equality 

Mathematics Subject Classification

62F12 62F30 62J10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceShandong Institute of Business and TechnologyYantaiChina
  2. 2.College of Economics and ManagementShanghai Maritime UniversityShanghaiChina

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