Relationship between ridge regression estimator and sample size when multicollinearity present among regressors
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The problem of multicollinearity is the most common problem in multiple regression models as in such cases, the ordinary least squares (OLS) estimator is inaccurately estimated. Of many methods suggested to solve the problem of multicollinearity, ridge regression method is a one of popular method. In this paper, simulation data with different level of correlation coefficient were generated using Monte Carlo techniques in SAS. The level of multicollinearity was detected by correlation matrix, variance influence factor (VIF) and condition number. The biased parameter (k) of ridge regression has been computed by using iterative method for ordinary ridge regression in different sample sizes. According to the results of this study, it was found that biased parameter (k) of ridge regression and sample sizes are significantly negatively correlated at level of 5% significance. This study would helpful to develop biased parameter table for different level of sample sizes in present of multicollinearity.
-  Alkhamisi, M., Khalaf, G. and Shukur, G. (2006). Some modifications for choosing ridge parameters. Communications in Statistics - Theory and Methods, 35(11), 2005-2020.
-  El-Dereny, M., Rashwan, N. I. (2011). Solving multicollinearity problem using ridge regression models, Int. J. Contemp. Math. Sci. 6, No. 9-12, 585-600.
-  Gibbons, D. G. (1981). A simulation study of some ridge estimators. Journal of the American Statistical Association, 76, 131-139.
-  Gujarati, D. N. (2004). Basic Econometrics, 4th edition, Tata McGraw-Hill, New Delhi.
-  Hocking, R. R., Speed, F. M. and Lynn, M. J. (1976). A class of biased estimators in linear regression. Technometrics, 18, 425-438.
-  Hoerl, A. E., Kennard, R. W. and Baldwin, K. F. (1975). Ridge regression: some simulation. Communications in Statistics, 4, 105-123.
-  Hoerl, A. E. and Kennard, R. W. (1970). Ridge Regression: Biased Estimation for Non-orthogonal Problems Regression Analysis and Biased Estimation. Technometrics, pp. 55-67.
-  Kennedy, P. (2003). A Guide to Econometrics, 5th edition, The MIT Press, Cambridge.
-  Khalaf, G. and Shukur, G. (2005). Choosing ridge parameters for regression problems. Communications in Statistics - Theory and Methods, 34, 1177-1182.
-  Kibria, B. M. G. (2003). Performance of some new ridge regression estimators. Communications in Statistics-Simulation and Computation, 32, 419-435.
-  McDonald, G. and Galarneau,D., (1975). A Monte Carlo evaluation of some ridge type estimators. Journal of the American Statistics Association, 70 (1975), 407-416.
-  Montgomery, D. C., Peck, E. A., Vining, G. G. (2001). Introduction to linear regression analysis, 3rd edition, Wiley, New York.
-  Muniz, G. and Kibria, B. M. G. (2009). On some ridge regression estimators: An empirical comparison. Communications in Statistics - Simulation and Computation, 38, 621-630.
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