Comparison of Covariance Matrices of Predictors in Seemingly Unrelated Regression Models

Nesrin Güler (), Melek Eriş Büyükkaya () and Melike Yiğit ()
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Nesrin Güler: Sakarya University
Melek Eriş Büyükkaya: Karadeniz Technical University
Melike Yiğit: Sakarya University

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 3, 801-809

Abstract: Abstract This paper considers comparison problems of predictor and estimator in the context of seemingly unrelated regression models ( $$\mathrm{SURM}$$ SURM s). $$\mathrm{SURM}$$ SURM s are a class of multiple regression equations with correlated errors among the equations from linear regression models. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors ( $$\mathrm{BLUP}$$ BLUP s) and the ordinary least squares predictors ( $$\mathrm{OLSP}$$ OLSP s) of unknown vectors under $$\mathrm{SURM}$$ SURM s by using various rank and inertia formulas of block matrices. The results for comparisons of the best linear unbiased estimators ( $$\mathrm{BLUE}$$ BLUE s) and the ordinary least squares estimators ( $$\mathrm{OLSE}$$ OLSE s) in the models are also considered.

Keywords: $$\mathrm{BLUP}$$ BLUP; Covariance matrix; Inertia; $$\mathrm{OLSP}$$ OLSP; Rank; Seemingly unrelated regression model; 62J05; 62H12; 15A03 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00174-w

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