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

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  • Shun Matsuura

    (Keio University)

  • Hiroshi Kurata

    (The University of Tokyo)

Abstract

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:29:y:2020:i:1:d:10.1007_s10260-019-00473-x
    DOI: 10.1007/s10260-019-00473-x
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    References listed on IDEAS

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    1. Henderson, Daniel J. & Kumbhakar, Subal C. & Li, Qi & Parmeter, Christopher F., 2015. "Smooth coefficient estimation of a seemingly unrelated regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 148-162.
    2. Marco Riani, 2004. "Robust multivariate transformations to normality: Constructed variables and likelihood ratio tests," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 13(2), pages 179-196, September.
    3. 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.
    4. 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.
    5. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 239-253.
    6. Soumaya, Moudar & Gaffke, Norbert & Schwabe, Rainer, 2015. "Optimal design for multivariate observations in seemingly unrelated linear models," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 48-56.
    7. 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.
    8. Liu, Aiyi, 2002. "Efficient Estimation of Two Seemingly Unrelated Regression Equations," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 445-456, August.
    9. 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.
    10. 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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    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.

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