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Best equivariant estimator of regression coefficients in a seemingly unrelated regression model with known correlation matrix


  • Hiroshi Kurata

    () (The University of Tokyo)

  • Shun Matsuura

    (Keio University)


Abstract This paper derives the best equivariant estimator (BEE) of the regression coefficients of a seemingly unrelated regression model with an elliptically symmetric error. Equivariance with respect to the group of location and scale transformations is considered. We assume that the correlation matrix of the error term is known. Since the correlation matrix is a maximal invariant parameter under the group action, the model treated in this paper is generated as exactly one orbit on the parameter space. It is also shown that the BEE can be viewed as a generalized least squares estimator.

Suggested Citation

  • Hiroshi Kurata & Shun Matsuura, 2016. "Best equivariant estimator of regression coefficients in a seemingly unrelated regression model with known correlation matrix," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(4), pages 705-723, August.
  • Handle: RePEc:spr:aistmt:v:68:y:2016:i:4:d:10.1007_s10463-015-0512-2
    DOI: 10.1007/s10463-015-0512-2

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    References listed on IDEAS

    1. Liu, Aiyi, 2002. "Efficient Estimation of Two Seemingly Unrelated Regression Equations," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 445-456, August.
    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.
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