Some remarks on comparison of predictors in seemingly unrelated linear mixed models

Nesrin Güler; Melek Eriş Büyükkaya

Applications of Mathematics (2022)

  • Volume: 67, Issue: 4, page 525-542
  • ISSN: 0862-7940

Abstract

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In this paper, we consider a comparison problem of predictors in the context of linear mixed models. In particular, we assume a set of m different seemingly unrelated linear mixed models (SULMMs) allowing correlations among random vectors across the models. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) of joint unknown vectors under SULMMs and their combined model. We use the matrix rank and inertia method for establishing equalities and inequalities. We also give an extensive approach for seemingly unrelated regression models (SURMs) by applying the results obtained for SULMMs to SURMs.

How to cite

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Güler, Nesrin, and Eriş Büyükkaya, Melek. "Some remarks on comparison of predictors in seemingly unrelated linear mixed models." Applications of Mathematics 67.4 (2022): 525-542. <http://eudml.org/doc/298319>.

@article{Güler2022,
abstract = {In this paper, we consider a comparison problem of predictors in the context of linear mixed models. In particular, we assume a set of $m$ different seemingly unrelated linear mixed models (SULMMs) allowing correlations among random vectors across the models. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) of joint unknown vectors under SULMMs and their combined model. We use the matrix rank and inertia method for establishing equalities and inequalities. We also give an extensive approach for seemingly unrelated regression models (SURMs) by applying the results obtained for SULMMs to SURMs.},
author = {Güler, Nesrin, Eriş Büyükkaya, Melek},
journal = {Applications of Mathematics},
keywords = {BLUP; covariance matrix; inertia; OLSP; rank; SULMM; SURM},
language = {eng},
number = {4},
pages = {525-542},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some remarks on comparison of predictors in seemingly unrelated linear mixed models},
url = {http://eudml.org/doc/298319},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Güler, Nesrin
AU - Eriş Büyükkaya, Melek
TI - Some remarks on comparison of predictors in seemingly unrelated linear mixed models
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 4
SP - 525
EP - 542
AB - In this paper, we consider a comparison problem of predictors in the context of linear mixed models. In particular, we assume a set of $m$ different seemingly unrelated linear mixed models (SULMMs) allowing correlations among random vectors across the models. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) of joint unknown vectors under SULMMs and their combined model. We use the matrix rank and inertia method for establishing equalities and inequalities. We also give an extensive approach for seemingly unrelated regression models (SURMs) by applying the results obtained for SULMMs to SURMs.
LA - eng
KW - BLUP; covariance matrix; inertia; OLSP; rank; SULMM; SURM
UR - http://eudml.org/doc/298319
ER -

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