Determining the Effect of Some Biasing Parameter Selection Methods for the Two Stage Ridge Regression Estimator

The use of biased estimation techniques is inevitable in connection with multicollinearity in simultaneous equations model. Two stage ridge estimator is a pioneer biased estimator which is used to recover the problems that are originated from the multicollinearity. The noteworthy issue regarding two stage ridge estimator is selection of its biasing parameter. Based on the works in the literature related to ridge estimator in a linear regression model, several methods on selection of the biasing parameter of the two stage ridge estimator are investigated in this paper. To demonstrate the best estimators of the biasing parameter, a Monte Carlo experiment is conducted. The utility of the proposed estimators of the biasing parameter for two stage ridge estimator is observed in terms of mean square error criterion.

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A. E. Hoerl and R. W. Kennard. “Ridge regression: biased estimation for nonorthogonal problems”. Technometrics. vol. 12. no. 1. pp. 55-67. 1970.

H. D. Vinod and A. Ullah. “Recent advances in regression methods”. Marcel Dekker. New York. Inc.. 1981.

A. E. Hoerl. R. W. Kennard and K. F. Baldwin. “Ridge regression: some simulations”. Communications in Statistics- Simulation and Computation. vol. 4. pp. 105– 123. 1975.

J. F. Lawless and P. A. Wang. “Simulation study of ridge and other regression estimators”. Communications in Statistics- Theory and Methods . vol. 5. no. 4. pp. 307- 323. 1976.

R. R. Hocking. F. M. Speed and M. J. Lynn. “A class of biased estimators in linear regression”. Technometrics. vol. 18. no. 4. pp. 425-437. 1976.

B. M. G. Kibria. “Performance of some new ridge regression estimators”. Communications in Statistics-Simulation and Computation. vol. 32. no. pp. 419–435. 2003.

G. Khalaf and G. Shukur. “Choosing ridge parameters for regression problems”. Communications in Statistics-Theory and Methods. vol. 34. pp. 1177-1182. 2005.

M. Alkhamisi. G. Khalaf and G. Shukur. “Some modifications for choosing ridge parameters”. Communications in Statistics- Theory and Methods. vol. 35. pp. 2005-2020. 2006.

M. Alkhamisi and G. Shukur. “Developing ridge parameters for SUR model”. Communications in Statistics-Theory and Methods. vol. 37. no. 4. pp. 544-564. 2008.

G. Muniz and B. M. G. Kibria. “On some ridge regression estimators: an empirical comparisons”. Communications in Statistics- Simulation and Computation. vol. 38. pp. 621- 630. 2009.

G. Muniz. B. M. G. Kibria. G. Shukur and K. Mansson. “On developing ridge regression parameters: a graphical investigation”. SORT. vol. 36. no. 2. pp. 115-138. 2012.

K. Mansson. G. Shukur and B. M. G Kibria. “A simulation study of some ridge regression estimators under different distributional assumptions”. Communications in Statistics- Simulation and Computation. vol. 39. no. 8. pp. 1639-1670. 2010.

H. M. Wagnar. “A monte carlo study of estimates of simultaneous linear structural equations”. Econometrica. vol. 26. pp. 117- 133. 1958.

D. F. Hendry. “The structure of simultaneous equation estimators”. Journal of Econometrics. vol. 4. pp. 51-88. 1976.

S. B. Park. “Some sampling properties of minimum expected loss (MELO) estimates of structural coefficients”. Journal of Econometrics. vol. 18. pp. 295–311. 1982.

O. Capps Jr and W. D. Grubbs. “A monte carlo study of collinearity in linear simultaneous equation models”. Journal of Statistical Computation and Simulation. vol. 39. pp. 139-162. 1991.

J. Johnston and J. E. Dinardo. “Econometric methods”. McGraw-Hill. New York. 1997.

J. Geweke. “Using simulation methods for bayesian econometric models: inference. development and communication”. Econometric Reviews. vol. 18. no. 1. pp. 1-73. 1999.

D. A. Agunbiade. “A monte carlo approach to the estimation of a just identified simultaneous three-equations model with three multicollinear exogenous variables”. Unpublished Ph.D. Thesis. University of Ibadan. 2007.

D. A. Agunbiade. “Effect of multicollinearity and the sensitivity of the estimation methods in simultaneous equation model”. Journal of Modern Mathematics and Statistics. vol. 5. no. 1. pp. 9-12. 2011.

D. A. Agunbiade and J. O. Iyaniwura. “Estimation under multicollinearity: a comparative approach using monte carlo methods”. Journal of Mathematics and Statistics. vol. 6 no. 2. pp. 183-192. 2010.