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Seemingly unrelated regression models. (English) Zbl 1274.62451
Seemingly unrelated regressions (SUR) proposed by 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 D.G. Fiebig [Seemingly unrelated regression. B.H. Baltagi, A companion to theoretical econometrics. Blackwell Publishing Ltd, Malden, MA, USA (2007)].

62J05 Linear regression; mixed models
62P20 Applications of statistics to economics
62F10 Point estimation
62H12 Estimation in multivariate analysis
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[1] B. Baltagi: On seemingly unrelated regression with error components. Econometrica 48 (1980), 1547–1552. · Zbl 0464.62104
[2] D. Davidson, J.G. MacKinnon: Estimation and Inference in Econometrics. Oxford University Press, New York, 1993. · Zbl 1009.62596
[3] J. Kmenta, R.F. Gilbert: Small sample properties of alternative estimators of seemingly unrelated regressions. J. Am. Stat. Assoc. 63 (1968), 1180–1200.
[4] L. Kubáček, L. Kubáčková, J. Volaufová: Statistical Models with Linear Structures. Veda, Bratislava, 1995.
[5] L. Kubáček: Multivariate Statistical Models Revisited. Palacky University, Olomouc, 2008.
[6] A.M. Kshirsagar: Multivariate Analysis. Marcel Dekker, Inc., New York, 1972.
[7] G.B. Mentz, A.M. Kshirsagar: Sum of profiles model with exchangeably distributed errors. Commun. Stat., Theory Methods 32 (2003), 1591–1605. · Zbl 1184.62090
[8] C.R. Rao, S.K. Mitra: Generalized Inverse of Matrices and its Applications. JohnWiley & Sons, New York-London-Sydney-Toronto, 1971. · Zbl 0236.15004
[9] C.R. Rao, J. Kleffe: Estimation of Variance Components and Applications. North-Holland, Amsterdam-New York-Oxford-Tokyo, 1988. · Zbl 0645.62073
[10] A. Zellner: Estimators of seemingly unrelated equations: Some exact finite sample results. J. Am. Stat. Assoc. 58 (1963), 977–992. · Zbl 0129.11203
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