Seemingly unrelated regression models.
type: Item
instance of: scholarly article
title: Seemingly unrelated regression models.
zbMATH Open document ID: 1274.62451
published in: Applications of Mathematics
publication date: 2013-05-13T00:00:00Z
full work available at URL: http://hdl.handle.net/10338.dmlcz/143137
review text: Seemingly unrelated regressions (SUR) proposed by \textit{A. Zellner} [J. Am. Stat. Assoc. 57, 348--368 (1962; Zbl 0113.34902)] are systems of equations that can be estimated one-by-one, but, due to a correlation among the error terms of the equations, efficient estimation is performed by generalized least squares applied to the whole system of equations. The estimation of SUR has been extensively studied by many authors and the presented work provides some explicit expressions for the special case of two regression equations with both univariate or multivariate responses. In particular, the formulas for the best linear unbiased estimator of the regression coefficients and estimates of the covariance structure (under homoscedasticity) are presented. Furthermore, the tests of equality of the coefficients in the two regression equations are derived. As the paper strictly concentrates on the statement and derivation of the results in the univariate and multivariate cases without more extensive discussion of more recent contributions to and developments of this stream of literature, an interested reader might complement the paper by reading, for example \textit{D.G. Fiebig} [Seemingly unrelated regression. B.H. Baltagi, A companion to theoretical econometrics. Blackwell Publishing Ltd, Malden, MA, USA (2007)].
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62P20
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62H12
zbMATH DE Number: 6162815
zbMATH Keywords: linear regression
zbMATH Keywords: best linear unbiased estimators
author: Lubomír Kubáček
MaRDI profile type: Publication
OpenAlex ID: W2095379833
cites work: On Seemingly Unrelated Regressions with Error Components
cites work: Q4802629
cites work: Sum of Profiles Model with Exchangeably Distributed Errors
cites work: Q5645536
cites work: Q4039798
cites work: Estimators for Seemingly Unrelated Regression Equations: Some Exact Finite Sample Results
DOI: 10.1007/S10492-013-0005-7
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description: scientific article; zbMATH DE number 6162815