Covariance matrix estimation in a seemingly unrelated regression model under Stein’s loss

  • Shun MatsuuraEmail author
  • Hiroshi Kurata
Original Paper


A seemingly unrelated regression model has been commonly used for describing a set of different regression models with correlations. This paper discusses the estimation of the covariance matrix in a seemingly unrelated regression model under Stein’s loss function. In particular, when the correlation matrix is assumed to be known, a best equivariant estimator of the covariance matrix is derived. Its properties are investigated and a connection to a best equivariant estimator of regression coefficients given in a previous study is shown. Results of numerical simulations and an illustrative example are also presented to compare the best equivariant estimator of the covariance matrix with several conventional covariance matrix estimators.


Correlation matrix Covariance matrix Equivariant estimator Generalized least squares estimator Seemingly unrelated regression model 



We would like to thank anonymous reviewers for constructive and helpful comments. This work was supported by JSPS KAKENHI Grant Number 15K15952.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Science and TechnologyKeio UniversityYokohamaJapan
  2. 2.Graduate School of Arts and SciencesThe University of TokyoMeguro-kuJapan

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