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Optimal estimator under risk matrix in a seemingly unrelated regression model and its generalized least squares expression

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  • Shun Matsuura

    (Keio University)

  • Hiroshi Kurata

    (The University of Tokyo)

Abstract

A set of multiple regression models whose error terms have possibly contemporaneous correlations is called a seemingly unrelated regression model. In this paper, a best equivariant estimator of the regression vector under risk matrix is established in a seemingly unrelated regression model. It should be noted that an estimator optimal with respect to risk matrix remains optimal under a broad range of quadratic loss functions. A generalized least squares expression of our estimator is also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:1:d:10.1007_s00362-021-01232-5
    DOI: 10.1007/s00362-021-01232-5
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    References listed on IDEAS

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    1. 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.
    2. Yuqin Sun & Rong Ke & Yongge Tian, 2014. "Some overall properties of seemingly unrelated regression models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 103-120, April.
    3. 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.
    4. M. Alkhamisi, 2010. "Simulation study of new estimators combining the SUR ridge regression and the restricted least squares methodologies," Statistical Papers, Springer, vol. 51(3), pages 651-672, September.
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    6. Liu, Aiyi, 2002. "Efficient Estimation of Two Seemingly Unrelated Regression Equations," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 445-456, August.
    7. 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.
    8. Ng, Vee Ming, 2002. "Robust Bayesian Inference for Seemingly Unrelated Regressions with Elliptical Errors," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 409-414, November.
    9. 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.
    10. Zhao, Li & Xu, Xingzhong, 2017. "Generalized canonical correlation variables improved estimation in high dimensional seemingly unrelated regression models," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 119-126.
    11. Jiang, Hong & Qian, Jianwei & Sun, Yuqin, 2020. "Best linear unbiased predictors and estimators under a pair of constrained seemingly unrelated regression models," Statistics & Probability Letters, Elsevier, vol. 158(C).
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