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

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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.

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Acknowledgments

The authors are grateful to two anonymous reviewers for their constructive comments. Kurata’s portion of this work was supported by JSPS KAKENHI Grant Number 26330035.

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Authors and Affiliations

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

    Hiroshi Kurata

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

    Shun Matsuura

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

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Kurata, H., Matsuura, S. Best equivariant estimator of regression coefficients in a seemingly unrelated regression model with known correlation matrix. Ann Inst Stat Math 68, 705–723 (2016). https://doi.org/10.1007/s10463-015-0512-2

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  • DOI: https://doi.org/10.1007/s10463-015-0512-2

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