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Computationally E.cient Methods for Solving SURE Models

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Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

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Abstract

Computationally efficient and numerically stable methods for solving Seemingly Unrelated Regression Equations (SURE) models are proposed. The iterative feasible generalized least squares estimator of SURE models where the regression equations have common exogenous variables is derived. At each iteration an estimator of the SURE 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, are also found to be efficient in the general case where the number of linear independent regressors is smaller than the number of observations.

This work is in part supported by the Swiss National Foundation Grants 21-54109.98 and 1214-056900.99/1.

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References

  1. E. Anderson, Z. Bai, and J. J. Dongarra. Generalized QR factorization and its applications. Linear Algebra and its Applications, 162:243–271, 1992.

    Article  MathSciNet  Google Scholar 

  2. H. C. Andrews and J. Kane. Kronecker matrices, computer implementation, and generalized spectra. Journal of the ACM, 17(2):260–268, 1970.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. J. Dhrymes. Topics in Advanced Econometrics, volume Vol.2: Linear and Nonlinear Simultaneous Equations. Springer-Verlag, New York, 1994.

    Google Scholar 

  4. Alexander Graham. Kronecker products and matrix calculus: with applications. Ellis Horwood Series in Mathematics and its Applications. Chichester: Ellis Horwood Limited, Publishers; New York etc.: Halsted Press: a division of John Wiley & Sons., 1986.

    Google Scholar 

  5. E. J. Kontoghiorghes. Parallel strategies for computing the orthogonal factorizations used in the estimation of econometric models. Algorithmica, 25:58–74, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  6. E. J. Kontoghiorghes. Parallel Algorithms for Linear Models: Numerical Methods and Estimation Problems, volume 15 of Advances in Computational Economics. Kluwer Academic Publishers, 2000.

    Google Scholar 

  7. E. J. Kontoghiorghes. Parallel strategies for solving SURE models with variance inequalities and positivity of correlations constraints. Computational Economics, 15(1+2):89–106, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  8. E. J. Kontoghiorghes and M. R. B. Clarke. An alternative approach for the numerical solution of seemingly unrelated regression equations models. Computational Statistics & Data Analysis, 19(4):369–377, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  9. E. J. Kontoghiorghes and E. Dinenis. Solving triangular seemingly unrelated regression equations models on massively parallel systems. In M. Gilli, editor, Computational Economic Systems: Models, Methods & Econometrics, volume 5 of Advances in Computational Economics, pages 191–201. Kluwer Academic Publishers, 1996.

    Google Scholar 

  10. E. J. Kontoghiorghes and E. Dinenis. Computing 3SLS solutions of simultaneous equation models with a possible singular variance-covariance matrix. Computational Economics, 10:231–250, 1997.

    Article  MATH  Google Scholar 

  11. S. Kourouklis and C. C. Paige. A constrained least squares approach to the general Gauss-Markov linear model. Journal of the American Statistical Association, 76(375):620–625, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  12. C. C. Paige. Numerically stable computations for general univariate linear models. Communications on Statistical and Simulation Computation, 7(5):437–453, 1978.

    Article  MathSciNet  Google Scholar 

  13. C. C. Paige. Fast numerically stable computations for generalized linear least squares problems. SIAM Journal on Numerical Analysis, 16(1):165–171, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  14. C. C. Paige. Some aspects of generalized QR factorizations. In M. G. Cox and S. J. Hammarling, editors, Reliable Numerical Computation, pages 71–91. Clarendon Press, Oxford, UK, 1990.

    Google Scholar 

  15. P. A. Regalia and S. K. Mitra. Kronecker products, unitary matrices and signal processing applications. SIAM Review, 31(4):586–613, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  16. V. K. Srivastava and T. D. Dwivedi. Estimation of seemingly unrelated regression equations Models: a brief survey. Journal of Econometrics, 10:15–32, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  17. V. K. Srivastava and D. E. A. Giles. Seemingly Unrelated Regression Equations Models: Estimation and Inference (Statistics: Textbooks and Monographs), volume 80. Marcel Dekker, Inc., 1987.

    Google Scholar 

  18. A. Zellner. An efficient method of estimating seemingly unrelated regression equations and tests for aggregation bias. Journal of the American Statistical Association, 57:348–368, 1962.

    Article  MATH  MathSciNet  Google Scholar 

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© 2001 Springer-Verlag Berlin Heidelberg

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Kontoghiorghes, E.J., Foschi, P. (2001). Computationally E.cient Methods for Solving SURE Models. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_57

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  • DOI: https://doi.org/10.1007/3-540-45262-1_57

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

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