Notes on Comparison of Covariance Matrices of BLUPs Under Linear Random-Effects Model with Its Two Subsample Models

  • Nesrin GülerEmail author
  • Melek Eriş Büyükkaya
Research Paper
Part of the following topical collections:
  1. Mathematics


A general linear random-effects model that includes both fixed and random effects, and its two subsample models are considered without making any restrictions on correlation of random effects and any full rank assumptions. Predictors of joint unknown parameter vectors under these three models have different algebraic expressions. Because of having different properties and performances under these models, it is one of the main focuses to make comparison of predictors. Covariance matrices of best linear unbiased predictors (BLUPs) of unknown parameters are used as a criterion to compare with other types predictors due to their definition of minimum covariance matrices structure. The comparison problem of covariance matrices of BLUPs under the models is considered in the study. We give a variety of equalities and inequalities in the comparison of covariance matrices of BLUPs of a general linear function of fixed effects and random effects under the models by using an approach consisting matrix rank and inertia formulas.


BLUE BLUP Covariance matrix Inertia Linear random-effects model Rank Subsample model 

Mathematics Subject Classification

62J05 62H12 15A03 



The authors are grateful to anonymous referees for their helpful comments.


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Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Department of StatisticsSakarya UniversitySakaryaTurkey
  2. 2.Department of MathematicsSakarya UniversitySakaryaTurkey

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