### 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.

Original language | English |
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Journal | Annals of the Institute of Statistical Mathematics |

DOIs | |

Publication status | Accepted/In press - 2015 Mar 12 |

### Fingerprint

### Keywords

- Equivariant estimator
- Generalized least squares estimator
- Group invariance
- Maximal invariant
- Seemingly unrelated regression model

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

**Best equivariant estimator of regression coefficients in a seemingly unrelated regression model with known correlation matrix.** / Kurata, Hiroshi; Matsuura, Shun.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Best equivariant estimator of regression coefficients in a seemingly unrelated regression model with known correlation matrix

AU - Kurata, Hiroshi

AU - Matsuura, Shun

PY - 2015/3/12

Y1 - 2015/3/12

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

UR - http://www.scopus.com/inward/record.url?scp=84924546458&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84924546458&partnerID=8YFLogxK

U2 - 10.1007/s10463-015-0512-2

DO - 10.1007/s10463-015-0512-2

M3 - Article

AN - SCOPUS:84924546458

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

ER -