Optimal estimator under risk matrix in a seemingly unrelated regression model and its generalized least squares expression

Shun Matsuura () and Hiroshi Kurata
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Shun Matsuura: Keio University
Hiroshi Kurata: The University of Tokyo

Statistical Papers, 2022, vol. 63, issue 1, No 5, 123-141

Abstract: Abstract A set of multiple regression models whose error terms have possibly contemporaneous correlations is called a seemingly unrelated regression model. In this paper, a best equivariant estimator of the regression vector under risk matrix is established in a seemingly unrelated regression model. It should be noted that an estimator optimal with respect to risk matrix remains optimal under a broad range of quadratic loss functions. A generalized least squares expression of our estimator is also presented.

Keywords: Elliptically symmetric distribution; Equivariant estimator; Generalized least squares; Risk matrix; Seemingly unrelated regression model; 62H12 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00362-021-01232-5

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