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Some remarks on comparison of predictors in seemingly unrelated linear mixed models. (English) Zbl 07584084

Summary: 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.

MSC:

62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
15A03 Vector spaces, linear dependence, rank, lineability
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