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

Hiroshi Kurata, Shun Matsuura

研究成果: Article

4 引用 (Scopus)

抄録

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.

元の言語English
ジャーナルAnnals of the Institute of Statistical Mathematics
DOI
出版物ステータスAccepted/In press - 2015 3 12

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Equivariant Estimator
Seemingly Unrelated Regression
Correlation Matrix
Regression Coefficient
Regression Model
Maximal Invariant
Equivariance
Generalized Least Squares Estimator
Group Action
Error term
Parameter Space
Orbit
Model

ASJC Scopus subject areas

  • Statistics and Probability

これを引用

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N2 - 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.

AB - 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.

KW - Equivariant estimator

KW - Generalized least squares estimator

KW - Group invariance

KW - Maximal invariant

KW - Seemingly unrelated regression model

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