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Comparison of Covariance Matrices of Predictors in Seemingly Unrelated Regression Models

Author

Listed:
  • Nesrin Güler

    (Sakarya University)

  • Melek Eriş Büyükkaya

    (Karadeniz Technical University)

  • Melike Yiğit

    (Sakarya University)

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.

Suggested Citation

  • Nesrin Güler & Melek Eriş Büyükkaya & Melike Yiğit, 2022. "Comparison of Covariance Matrices of Predictors in Seemingly Unrelated Regression Models," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(3), pages 801-809, September.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:3:d:10.1007_s13226-021-00174-w
    DOI: 10.1007/s13226-021-00174-w
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    References listed on IDEAS

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