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

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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.

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  • 22 January 2021

    There are mistakes in the author’s name on the Springer webpage on original upload.

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Acknowledgments

The authors would like to thank the anonymous referees for their careful reading of the paper and their valuable remarks.

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Authors and Affiliations

  1. Department of Econometrics, Sakarya University, TR-54187, Sakarya, Turkey

    Nesrin Güler

  2. Department of Statistics and Computer Sciences, Karadeniz Technical University, TR-61080, Trabzon, Turkey

    Melek Eriş Büyükkaya

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  1. Nesrin Güler
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  2. Melek Eriş Büyükkaya
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Correspondence to Nesrin Güler.

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Güler, N., Eriş Büyükkaya, M. Some remarks on comparison of predictors in seemingly unrelated linear mixed models. Appl Math 67, 525–542 (2022). https://doi.org/10.21136/AM.2021.0366-20

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  • DOI: https://doi.org/10.21136/AM.2021.0366-20

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