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

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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.

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Acknowledgements

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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Authors and Affiliations

  1. Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan

    Shun Matsuura

  2. Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8902, Japan

    Hiroshi Kurata

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  1. Shun Matsuura
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  2. Hiroshi Kurata
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Correspondence to Shun Matsuura.

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Matsuura, S., Kurata, H. Covariance matrix estimation in a seemingly unrelated regression model under Stein’s loss. Stat Methods Appl 29, 79–99 (2020). https://doi.org/10.1007/s10260-019-00473-x

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