Seemingly Unrelated Regressions Models With Reduced Ranks

  • Gregory C. Reinsel
  • Raja P. Velu
Part of the Lecture Notes in Statistics book series (LNS, volume 136)


The classical multivariate linear regression model discussed in Chapter 1 can be generalized by allowing the different response variables y ik to have different input or predictor variables X ik = (x i1k ,... , x ink ,)’ for different i, so that y ik - X’ ik C (i) + ∈ ik , i = 1,... ,m, and the errors ik are contemporaneously correlated across the different response variables. Multivariate linear regression models of this form were considered by Zellner (1962), who referred to them as seemingly unrelated regression (SUR) equations models. In experimental design situations, the model is also referred to as the multiple design multivariate linear model (e.g., Srivastava, 1967; Roy, Gnanadesikan, and Srivastava, 1971). In the notation of Section 1.2, the linear regression model for the T × 1 vector of values for the ith response variable is
$${Y_{(i)}} = {X_i}^\prime {C_{(i)}} + { \in _{(i)}},\quad for\quad i = 1, \ldots ,m$$
where X i = [X i1 , ..., X iT ] is n × T, while Y (i) = (y i1 ,... ,y iT )’, i = ( i1 ,... ∈ iT )’, and C (i) are the same as in the previous model of Chapter 1.


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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Gregory C. Reinsel
    • 1
  • Raja P. Velu
    • 2
  1. 1.Department of StatisticsUniversity of Wisconsin, MadisonMadisonUSA
  2. 2.School of ManagementSyracuse UniversitySyracuseUSA

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