Numerical and Computational Strategies for Solving Seemingly Unrelated Regression Models

  • Paolo Foschi
  • Lucien Garin
  • Erricos J. Kontoghiorghes
Part of the Applied Optimization book series (APOP, volume 74)


Computationally efficient and numerically stable methods for solving Seemingly Unrelated Regression (SUR) models are proposed. The iterative feasible generalized least squares estimator of SUR módels where the regression equations have common exogenous variables is derived. At each iteration an estimator of the SUR model is obtained from the solution of a generalized linear least squares problem. The proposed methods, which have as a basic tool the generalized QR decomposition (GQRD), are also found to be efficient in the general case where the number of linear independent regressors is smaller than the number of observations.

Parallel strategies based on compound disjoint Givens rotations are designed for computing the main two factorizations that are used in the GQRD. The first factorization requires the triangularization of a set of upper-triangular after deleting columns. The second factorization is equivalent in updating a lower-triangular matrix with a matrix having a block lower-triangular structure. Theoretical measures of complexity and examples are used for comparing and investigating the various parallel strategies.


SUR models Matrix factorizations Kronecker products Parallel algorithms 


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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Paolo Foschi
    • 1
  • Lucien Garin
    • 1
  • Erricos J. Kontoghiorghes
    • 1
  1. 1.Institut d’informatiqueUniversité de NeuchâtelNeuchâtelSwitzerland

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