American Journal of Theoretical and Applied Statistics
Volume 4, Issue 3, May 2015, Pages: 150-155
Received: Apr. 4, 2015;
Accepted: Apr. 14, 2015;
Published: Apr. 24, 2015
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Shohel Rana, Department of Mathematics and Natural Sciences, BRAC University, Dhaka, Bangladesh
Mohammad Mastak Al Amin, Department of Mathematics and Natural Sciences, BRAC University, Dhaka, Bangladesh
This paper proposed a transformed method of SUR model which provided unbiased estimation in case of two and three equations of high and low co-linearity for both small and large datasets. The generalized least squares (GLS) method for estimation of seemingly unrelated regression (SUR) model proposed by Zellner (1962), Srivastava and Giles (1987),provided higher MSE. Although the Ridge estimators proposed by Alkhamisi and Shukur (2008) provided smaller MSE in comparison with others, it was not unbiased in case of severe multicollinearity.This study showed that our proposed method typically provided unbiasedestimator with lower MSE and TMSE than traditional methods.
Mohammad Mastak Al Amin,
An Alternative Method of Estimation of SUR Model, American Journal of Theoretical and Applied Statistics.
Vol. 4, No. 3,
2015, pp. 150-155.
Alan J. L. 2004.Matrix Analysis for Scientists and Engineers. Society for Industrial and Applied Mathematics: 139-140.
Ali M. I. 1984. Matrices and Linear Transformations. International Student Edition: 45-212.
Alkhamisi M. A, Shukur G. 2008. Developing Ridge Parameters for SUR Model,Communications in Statistics - Theory and Methods,80:544-564.
Anderson T. W. 1984. AnIntroduction to Multivariate Statistical Analysis. John Wiley and Sons, Inc., New York, Second edition:675.
Dereny M. El, Rashwan N. I. 2011. Solving Multicollinearity Problem Using Ridge Regression Models. Int. J. Contemp. Math. Sciences, 6:585 – 600.
Dwivedi T. D, Srivastava V. K. 1978. Optimality of least squares in the seemingly unrelated regression equation model. Journal of Econometrics, 7: 391-395.
Gujarati D. N. 1995. Basic Econometrics. McGraw-Hill, New York. Third edition: 826. Hubert M, Verdonck T, O. Yorulmaz O. Preprint.
Johnston J, DiNardo J. 1963, 1972 and 1984. Econometric Methods. McGRAW-HILL INTERNATIONAL EDITIONS Fourth edition: 531.
Maddala G. S. 1988. Introduction to Econometrics, Macmillan international editions: 364-365.
Ebukuyo O. B, Adepoju A. A, Olamide E. I. 2013.Bootstrap Approach for Estimating Seemingly Unrelated Regressions with Varying Degree of Autocorrelated Disturbances. Journal of Progress in Applied Mathematics, 5:55-63.
Parks R. W.1967. Efficient Estimation of a System of Regression Equations When Disturbances are Both Serially and Contemporaneously Correlated. Journal of theAmerican Statistical Association 62: 500-509.
Rahman M. 2008. Basic Econometrics, Theory and Practice, The University Grants Commission Dhaka. First edition.
Srivastava V, Giles D. 1987. Seemingly Unrelated Regression Equations Models. New York: Marcel Dekker.
Stewart G. W. 1980. The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimators. SIAM J. Numer. Anal.17 (3): 403–409.
Zeebari Z, Shukur G. 2012. On the Least Absolute Deviations Method for Ridge Estimation of SURE Models.In:Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415XArticle in journal.
Zellner A. 1962. An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. Journal of the American Statistical Association, 57: 348-368.
Zellner A. 1963. Estimators for seemingly unrelated regression equations: some exact finite sample results. Journal of the American Statistical Association, 58: 977-992.