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

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 shoul...

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Bibliographic Details
Published inStatistical papers (Berlin, Germany) Vol. 63; no. 1; pp. 123 - 141
Main Authors Matsuura, Shun, Kurata, Hiroshi
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2022
Springer Nature B.V
Subjects
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Hypotheses
Insurance
Least squares
Management
Mathematical analysis
Mathematics and Statistics
Multiple regression models
Operations Research/Decision Theory
Probability Theory and Stochastic Processes
Quality control
Regular Article
Risk
Statistics
Statistics for Business
Seemingly unrelated regression model
Elliptically symmetric distribution
Generalized least squares
Risk matrix
62H12
Equivariant estimator
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Summary: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.
ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-021-01232-5