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Rank and inertia formulas for covariance matrices of BLUPs in general linear mixed models

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  • Nesrin Güler
  • Melek Eriş Büyükkaya

Abstract

We consider an extended general linear model containing new observations without making any restrictions on correlation of random vectors and any rank assumptions. We give variety of equalities and inequalities in the comparison of covariance matrix of BLUP of new observations with any other unbiased predictors’ covariance matrices by using rank and inertia formulas. We next consider the general linear mixed model under the assumption that the random effects and the random errors can be correlated. Using connection between the general linear mixed model and the extended general linear model, we give some equalities and inequalities for comparing the covariance matrices of BLUP of linear function of fixed and random effects with covariance matrices of any other type of unbiased predictors. We also give results for special cases and for linear function of partial fixed and random effects.

Suggested Citation

  • Nesrin Güler & Melek Eriş Büyükkaya, 2020. "Rank and inertia formulas for covariance matrices of BLUPs in general linear mixed models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(21), pages 4997-5012, September.
    • Handle: RePEc:taf:lstaxx:v:50:y:2020:i:21:p:4997-5012
    DOI: 10.1080/03610926.2019.1599950
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