Covariance matrix estimation in a seemingly unrelated regression model under Stein’s loss

Shun Matsuura, Hiroshi Kurata

Research output: Contribution to journalArticle

Abstract

A seemingly unrelated regression model has been commonly used for describing a set of different regression models with correlations. This paper discusses the estimation of the covariance matrix in a seemingly unrelated regression model under Stein’s loss function. In particular, when the correlation matrix is assumed to be known, a best equivariant estimator of the covariance matrix is derived. Its properties are investigated and a connection to a best equivariant estimator of regression coefficients given in a previous study is shown. Results of numerical simulations and an illustrative example are also presented to compare the best equivariant estimator of the covariance matrix with several conventional covariance matrix estimators.

Original languageEnglish
JournalStatistical Methods and Applications
DOIs
Publication statusPublished - 2019 Jan 1

Fingerprint

Covariance Matrix Estimation
Seemingly Unrelated Regression
Equivariant Estimator
Covariance matrix
Regression Model
Correlation Matrix
Regression Coefficient
Loss Function
Estimator
Numerical Simulation
Regression model
Seemingly unrelated regression
Covariance matrix estimation

Keywords

  • Correlation matrix
  • Covariance matrix
  • Equivariant estimator
  • Generalized least squares estimator
  • Seemingly unrelated regression model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

@article{3ff1edb2581f4b66b898ac3aaaeb27bb,
title = "Covariance matrix estimation in a seemingly unrelated regression model under Stein’s loss",
abstract = "A seemingly unrelated regression model has been commonly used for describing a set of different regression models with correlations. This paper discusses the estimation of the covariance matrix in a seemingly unrelated regression model under Stein’s loss function. In particular, when the correlation matrix is assumed to be known, a best equivariant estimator of the covariance matrix is derived. Its properties are investigated and a connection to a best equivariant estimator of regression coefficients given in a previous study is shown. Results of numerical simulations and an illustrative example are also presented to compare the best equivariant estimator of the covariance matrix with several conventional covariance matrix estimators.",
keywords = "Correlation matrix, Covariance matrix, Equivariant estimator, Generalized least squares estimator, Seemingly unrelated regression model",
author = "Shun Matsuura and Hiroshi Kurata",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/s10260-019-00473-x",
language = "English",
journal = "Statistical Methods and Applications",
issn = "1618-2510",
publisher = "Physica-Verlag",

}

TY - JOUR

T1 - Covariance matrix estimation in a seemingly unrelated regression model under Stein’s loss

AU - Matsuura, Shun

AU - Kurata, Hiroshi

PY - 2019/1/1

Y1 - 2019/1/1

N2 - A seemingly unrelated regression model has been commonly used for describing a set of different regression models with correlations. This paper discusses the estimation of the covariance matrix in a seemingly unrelated regression model under Stein’s loss function. In particular, when the correlation matrix is assumed to be known, a best equivariant estimator of the covariance matrix is derived. Its properties are investigated and a connection to a best equivariant estimator of regression coefficients given in a previous study is shown. Results of numerical simulations and an illustrative example are also presented to compare the best equivariant estimator of the covariance matrix with several conventional covariance matrix estimators.

AB - A seemingly unrelated regression model has been commonly used for describing a set of different regression models with correlations. This paper discusses the estimation of the covariance matrix in a seemingly unrelated regression model under Stein’s loss function. In particular, when the correlation matrix is assumed to be known, a best equivariant estimator of the covariance matrix is derived. Its properties are investigated and a connection to a best equivariant estimator of regression coefficients given in a previous study is shown. Results of numerical simulations and an illustrative example are also presented to compare the best equivariant estimator of the covariance matrix with several conventional covariance matrix estimators.

KW - Correlation matrix

KW - Covariance matrix

KW - Equivariant estimator

KW - Generalized least squares estimator

KW - Seemingly unrelated regression model

UR - http://www.scopus.com/inward/record.url?scp=85066491253&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066491253&partnerID=8YFLogxK

U2 - 10.1007/s10260-019-00473-x

DO - 10.1007/s10260-019-00473-x

M3 - Article

AN - SCOPUS:85066491253

JO - Statistical Methods and Applications

JF - Statistical Methods and Applications

SN - 1618-2510

ER -