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On the Efficiencies of Several Generalized Least Squares Estimators in a Seemingly Unrelated Regression Model and a Heteroscedastic Model

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  • Kurata, Hiroshi

Abstract

This paper investigates the efficiencies of several generalized least squares estimators (GLSEs) in terms of the covariance matrix. Two models are analyzed: a seemingly unrelated regression model and a heteroscedastic model. In both models, we define a class of unbiased GLSEs and show that their covariance matrices remain the same even if the distribution of the error term deviates from the normal distributions. The results are applied to the problem of evaluating the lower and upper bounds for the covariance matrices of the GLSEs.

Suggested Citation

  • Kurata, Hiroshi, 1999. "On the Efficiencies of Several Generalized Least Squares Estimators in a Seemingly Unrelated Regression Model and a Heteroscedastic Model," Journal of Multivariate Analysis, Elsevier, vol. 70(1), pages 86-94, July.
    • Handle: RePEc:eee:jmvana:v:70:y:1999:i:1:p:86-94
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    Citations

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    Cited by:

    1. Shun Matsuura & Hiroshi Kurata, 2022. "Optimal estimator under risk matrix in a seemingly unrelated regression model and its generalized least squares expression," Statistical Papers, Springer, vol. 63(1), pages 123-141, February.
    2. Zellner, Arnold & Ando, Tomohiro, 2010. "A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model," Journal of Econometrics, Elsevier, vol. 159(1), pages 33-45, November.
    3. Xu, Qinfeng & You, Jinhong & Zhou, Bin, 2008. "Seemingly unrelated nonparametric models with positive correlation and constrained error variances," Economics Letters, Elsevier, vol. 99(2), pages 223-227, May.
    4. Radhey S. Singh & Lichun Wang, 2012. "A Note on Estimation in Seemingly Unrelated Semi-Parametric Regression Models," Journal of Quantitative Economics, The Indian Econometric Society, vol. 10(1), pages 56-69, January.
    5. Jinhong You & Xian Zhou, 2010. "Statistical inference on seemingly unrelated varying coefficient partially linear models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(2), pages 227-253, May.
    6. Shun Matsuura & Hiroshi Kurata, 2020. "Covariance matrix estimation in a seemingly unrelated regression model under Stein’s loss," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 79-99, March.
    7. Kurata, Hiroshi, 2004. "One-sided tests for independence of seemingly unrelated regression equations," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 393-406, August.

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