Abstract
The problem of computing estimates of parameters in SURE models withvariance inequalities and positivity of correlations constraintsis considered. Efficient algorithms that exploit the blockbi-diagonal structure of the data matrix are presented. Thecomputational complexity of the main matrix factorizations isanalyzed. A compact method to solve the model with proper subsetregressors is proposed.
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References
Arellano, M. (1989). On the efficient estimation of simultaneous equations with covariance restrictions. Journal of Econometrics, 42, 247-265.
Bischof, C. and Van Loan, C.F. (1987). The WY representation for products of Householder matrices. SIAM Journal on Scientific and Statistical Computing, 8 (1), 2-13.
Björck, Å. (1996). Numerical Methods for Least Squares Problems. SIAM, Philadelphia.
Björck, Å. and Paige, C.C. (1994). Solution of augmented linear systems using orthogonal factorizations. BIT, 34, 1-26.
Blackford, L.S., Choi, J., Cleary, A., D'Azevedo, E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D. and Whaley, R. (1997). ScaLAPACK Users' Guide. SIAM, Philadelphia.
Gill, P.E., Golub, G.H., Murray, W. and Saunders, M.A. (1974). Methods for modifying matrix factorizations. Mathematics of Computation, 28 (126), 505-535.
Golub, G.H. and Van Loan, C.F. (1996). Matrix Computations, 3rd Edition, Johns Hopkins University Press, Baltimore, Md.
Gulliksson, M. (1994). Iterative refinement for constrained and weighted linear least squares. BIT, 34, 239-253.
Gulliksson, M. and Wedin, P.-Å. (1992). Modifying the QR decomposition to constrained and weighted linear least squares. SIAM Journal on Matrix Analysis and Applications, 13 (4), 1298-1313.
Hausman, J.A., Newey, W.K. and Taylor, W.E. (1987). Efficient estimation and identification of simultaneous equation models with covariance restrictions. Econometrica, 55, 849-874.
Kontoghiorghes, E.J. (1995). New parallel strategies for block updating the QR decomposition. Parallel Algorithms and Applications, 5 (1+2), 229-239.
Kontoghiorghes, E.J. (1999). Parallel strategies for computing the orthogonal factorizations used in the estimation of econometric models. Algorithmica (special issue on Computational Finance), 25, 58-74.
Kontoghiorghes, E.J. and Clarke, M.R.B. (1993a). Parallel reorthogonalization of the QR decomposition after deleting columns. Parallel Computing, 19 (6), 703-707.
Kontoghiorghes, E.J. and Clarke, M.R.B. (1993b). Solving the updated and downdated ordinary linear model on massively parallel SIMD systems. Parallel Algorithms and Applications, 1 (2), 243-252.
Kontoghiorghes, E.J. and Clarke, M.R.B. (1995). An alternative approach for the numerical solution of seemingly unrelated regression equation models. Computational Statistics & Data Analysis, 19 (4), 369-377.
Kontoghiorghes, E.J. and Dinenis, E. (1994). Implementation and performance evaluation of massively parallel algorithms for block updating least squares. In V. Prasana, V. Bhatkar, L. Patnaik and S. Tripathi (eds.), Parallel Processing (Proceedings of the IEEE 1st IWPP), pp. 705-710.
Kontoghiorghes, E.J. and Dinenis, E. (1996). Solving triangular seemingly unrelated regression equation models on massively parallel systems. In M. Gilli (ed.), Computational Economic Systems: Models, Methods & Econometrics, Vol. 5 of Advances in Computational Economics, pp. 191-201.
Kontoghiorghes, E.J. and Dinenis, E. (1997a). Computing 3SLS solutions of simultaneous equation models with a possible singular variance-covariance matrix. Computational Economics, 10, 231-250.
Kontoghiorghes, E.J. and Dinenis, E. (1997b). Towards the parallel implementation of the SURE model estimation algorithm. Journal of Mathematical Modelling and Scientific Computing, 8, 335-341.
Lawson, C.L. and Hanson, R.J. (1974). Solving Least Squares Problems. Prentice-Hall Englewood Cliffs.
Regalia, P. and Mitra, S. (1989). Kronecker products, unitary matrices and signal processing applications. SIAM Review, 31 (4), 586-613.
Rothenberg, T.J. and Ruud, P.A. (1990). Simultaneous equations with covariance restrictions. Journal of Econometrics, 44, 25-39.
Schott, J.R. (1997). Matrix Analysis for Statistics (Wiley series in probability and statistics). John Wiley and Sons, Inc.
Schreiber, R. and Van Loan, C.F. (1989). A Storage Efficient WY representation for products of Householder transformations. SIAM Journal on Scientific and Statistical Computing, 10, 53-57.
Srivastava, V.K. and Giles, D.E.A. (1987). Seemingly Unrelated Regression Equations Models: Estimation and Inference (Statistics: Textbooks and Monographs), Vol. 80. Marcel Dekker, Inc.
Swanson, N.R. and Grange, C.W.J. (1997). Impulse response functions based on a causal approach to residual orthogonalization in vector autoregressions. Journal of the American Statistical Association, 92 (437), 357-367.
Zellner, A. (1979). An error-components procedure (ECP) for introducing prior information about covariance matrices and analysis of multivariate regression models. International Economic Review, 20 (3), 679-692.
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Kontoghiorghes, E.J. Parallel Strategies for Solving SURE Models with Variance Inequalities and Positivity of Correlations Constraints. Computational Economics 15, 89–106 (2000). https://doi.org/10.1023/A:1008647128446
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DOI: https://doi.org/10.1023/A:1008647128446