Geodesic
Some remarks on comparison of predictors in seemingly unrelated linear mixed models
Applications of Mathematics, Tome 67 (2022) no. 4, pp. 525-542.

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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.
DOI : 10.21136/AM.2021.0366-20
Classification : 15A03, 62H12, 62J05
Keywords: BLUP; covariance matrix; inertia; OLSP; rank; SULMM; SURM 
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Güler, Nesrin; Eriş Büyükkaya, Melek. Some remarks on comparison of predictors in seemingly unrelated linear mixed models. Applications of Mathematics, Tome 67 (2022) no. 4, pp. 525-542. doi : 10.21136/AM.2021.0366-20. http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0366-20/

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