Effects of Atypical Observations on the Estimation of Seemingly Unrelated Regression Model

A. A. Adepoju^1, and A. O. Akinwumi¹

¹Department of Statistics, University of Ibadan, Ibadan, Nigeria

Cite this paper:
A. A. Adepoju and A. O. Akinwumi. Effects of Atypical Observations on the Estimation of Seemingly Unrelated Regression Model. Journal of Mathematical Sciences and Applications. 2017; 5(2):30-35. doi: 10.12691/jmsa-5-2-1

Abstract

The Seemingly Unrelated Regression Equation model is a generalization of a linear regression model that consists of several regression equations in order to achieve efficient estimates. Unfortunately, the assumptions underlying most SUR estimators give little/no consideration to outlying observations which may be present in the data. These atypical observations may have some apparent distorting effects on the estimates produced by these estimators. This study thus examined the effect of outliers on the performances of SUR and OLS estimators using Monte Carlo simulation method. The Cholesky method was used to partition the variance-covariance matrix by decomposing it into the upper and lower non-singular triangular matrices. Varying degree of outliers; 0%, 5%, and 10% were each introduced into five sample sizes; 20, 40, 60, 100 and 500 respectively. The performances of the estimators were evaluated using Absolute Bias (ABIAS) and Mean Square Error (MSE). The results showed that at 0% outliers (when outliers were absent), the ABIAS and MSE of the SUR and OLS estimators showed similar results. At 5% and 10% outliers, the magnitude in ABIAS and MSE for both estimators increased but the SUR estimator showed better performance than the OLS estimator. As the sample size increases, ABIAS and MSE of the estimators decreased consistently for the various degrees of outliers considered with SUR consistently better than OLS.

Keywords:
Seemingly Unrelated Regression outliers Monte Carlo Mean Square Error Absolute Bias

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References:

[1]	Zellner A. (1962): An Efficient Method of Estimating Seemingly Unrelated Regression Equations and Tests of Aggregation Bias, Journal of the American Statistical Association, 57 (298): 348-368; 500-509.
[2]	Galimberti Giuliano, Scardovi Elena, Soffritti Gabriele (2014): Using mixtures in seemingly unrelated linear regression models with non-normal errors, Department of Statistical Sciences, University of Bologna.
[3]	Judge, G. G., Hill, R. C., Grittiths, W. E., Liitkepohl, H. and. Lee, T.. C. (1985): The Theory and Practice of Econometrics, 2nd Edition. Wiley, New York.
[4]	Srivastava, V. K. and D. E. A. Giles (1987): Seemingly Unrelated Regression Equations Models, New York: Marcel Dekker Inc.
[5]	Zellner, A. (1963): Estimators for seemingly unrelated regression equations: some exact finite sample results. J. Am. Stat. Assoc. 58, 977-992.
[6]	Kmenta, J., Gilbert, R. (1968): Small sample properties of alternative estimators of seemingly unrelated regressions. J. Am. Stat. Assoc. 63, 1180-1200.
[7]	Oberhofer, W., Kmenta, J. (1974): A general procedure for obtaining maximum likelihood estimates in generalized regression models. Econometrica 42, 579-590.
[8]	Magnus, J. R. (1978): Maximum likelihood estimation of the GLS model with unknown parameters in the disturbance covariance matrix. J. Econom. 7, 281-312.
[9]	Park, T. (1993): Equivalence of maximum likelihood estimation and iterative two-stage estimation for seemingly unrelated regression models. Commun. Stat. Theory 22, 2285-2296.
[10]	Rocke, D. (1989): Bootstrap Bartlett adjustment in seemingly unrelated regression. J. Am. Stat. Assoc. 84, 598-601.
[11]	Rilstone, P., Veall, M. (1996): Using bootstrapped confidence intervals for improved inferences with seemingly unrelated regression equations. Econom. Theory 12, 569-580.
[12]	Binkley, J.K. and Nelson, C.H. (1988): a note on the efficiency of seemingly unrelated regression. The American Statistician 42(2): 137-139.
[13]	Conniffe, D. (1982): A note on seemingly unrelated regressions. Econometrica 50(1): 229-233.
[14]	Moon, Hyungsik Roger and Perron, Benoit (2006): seemingly unrelated regression Models.
[15]	Viraswami k. (1998): Some efficiency results on Seemingly Unrelated Regression Equations.
[16]	Binkley J. K, (1982): Journal of the American Statistical Association Vol 77:890-895.
[17]	Bartels, R. and Fie big, D.G. (1991): A simple characterization of seemingly unrelated regressions model in which OLS is BLUE. The American Statistician 45(2): 137-140 5.
[18]	Rousseeuw P.J. and Leroy A.M. (1987): Robust Regression and Outlier Detection.
[19]	Zimmerman, D. W. (1998): Invalidation of parametric and nonparametric statistical tests by concurrent violation of two assumptions. Journal of Experimental Education, 67 (1), 55-68.
[20]	Mishra, S. K. (2008): Robust Two-Stage Least Squares: Some Monte Carlo Experiments. MPRA Paper No. 9737M. (Online at http://mpra.ub.uni-muenchen.de/9737/)
[21]	Osborne, J. W, Christian, W. R. I, & Gunter, J. S. (2001): Educational psychology from a statistician’s perspective: A review of the quantitative quality of our field. Paper presented at the Annual Meeting of the American Educational Research Association, Seattle, WA.
[22]	Adepoju, A. A. and Olaomi, J. O. (2012): Evaluation of Small Sample Estimators of Outliers Infested Simultaneous Equation Model: A Monte Carlo Approach. Journal of Applied Economic Sciences Vol. 7. No. 1: 8-16.
[23]	Oseni, B. M. and Adepoju, A. A. (2011): Assessment of Simultaneous Equation Techniques under the Influence of Outliers. Journal of The Nigerian Statistical Association Vol. 23: 1-9.