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


Guler N., Buyukkaya M. E.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1080/03610926.2021.1967397
  • Title of Journal : COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Keywords: BLUP, covariance matrix, inertia, linear mixed model, rank, transformed model, UNBIASED PREDICTION, EQUALITIES, COMPONENTS, ESTIMATORS, MATRICES, FORMULAS, BLUES

Abstract

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.