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

Shun Matsuura; Hiroshi Kurata

doi:10.1007/s00362-021-01232-5

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

Shun Matsuura, Hiroshi Kurata

Department of Industrial and Systems Engineering

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	Statistical Papers
DOIs	https://doi.org/10.1007/s00362-021-01232-5
Publication status	Accepted/In press - 2021

Keywords

Elliptically symmetric distribution
Equivariant estimator
Generalized least squares
Risk matrix
Seemingly unrelated regression model

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s00362-021-01232-5

Cite this

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

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",

author = "Shun Matsuura and Hiroshi Kurata",

note = "Funding Information: The authors would like to thank anonymous reviewers for many constructive and useful comments. Matsuura{\textquoteright}s portion of this work is supported by JSPS KAKENHI Grant Number 20K11713. Kurata{\textquoteright}s portion of this work is supported by JSPS KAKENHI Grant Number 19K11853. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

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AU - Matsuura, Shun

AU - Kurata, Hiroshi

N1 - Funding Information: The authors would like to thank anonymous reviewers for many constructive and useful comments. Matsuura’s portion of this work is supported by JSPS KAKENHI Grant Number 20K11713. Kurata’s portion of this work is supported by JSPS KAKENHI Grant Number 19K11853. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2021

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N2 - 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.

AB - 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.

KW - Elliptically symmetric distribution

KW - Equivariant estimator

KW - Generalized least squares

KW - Risk matrix

KW - Seemingly unrelated regression model

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

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Keywords

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