Inertia and rank approach in transformed linear mixed models for comparison of BLUPs

Guler N., Buyukkaya M. E.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.52, no.9, pp.3108-3123, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 9
  • Publication Date: 2023
  • Doi Number: 10.1080/03610926.2021.1967397
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Business Source Elite, Business Source Premier, CAB Abstracts, Compendex, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.3108-3123
  • Keywords: BLUP, covariance matrix, inertia, linear mixed model, rank, transformed model, UNBIASED PREDICTION, EQUALITIES, COMPONENTS, ESTIMATORS, MATRICES, FORMULAS, BLUES
  • Karadeniz Technical University Affiliated: Yes


This paper is concerned with comparison problems of predictors between a linear mixed model (LMM) that includes both fixed and random effects and its transformed model under general assumptions. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) of unknown vectors under the models by using various inertia and rank formulas of block matrices. We also give some results for special transformed models such as submodels of original LMMs by applying the results obtained for general cases.