In a linear regression model, it is often assumed that the explanatory variables are independent.This assumption is often violated and Ridge Regression estimator introduced by Hoerl and Kennard (1970)has been identified to be more efficient than ordinary least square (OLS) in handling it. However, it requiresa ridge parameter, K, of which many have been proposed. In this study, estimators based on Hoerl andKennard were classified into different forms and various types and some modifications were proposed toimprove it. Investigation were done by conducting 1000 Monte-Carlo experiments under five (5) levels ofmulticollinearity, three (3) levels of error variance and five levels of sample size. For the purpose of comparingthe performance of the improved ridge parameter with the existing ones, the number of times the MSE ofthe improved ridge parameter is less than the existing ones is counted over the levels of multicollinearity (5)and error variance (3). Also, a maximum of fifteen (15) counts is expected. Results show that the improvedridge parameters proposed in this study are better than the existing ones most especially with the quantity
References
Alkhamisi, M., Khalaf, G. and Shukur, G. (2006). Some modifications for choosing ridge parameters,
Communications in Statistics- Theory and Methods, 35(11), 2005-2020.
Alkhamisi, M. and Shukur, G. (2007). A Monte Carlo study of recent ridge parameters, Commun. Statist.
Simulation and Computation, 36(3), 535-547. Dorugade, A. V. (2014). On comparison of some ridge parameters in Ridge Regression, Sri Lankan
Journal of Applied Statistics, 15(1), 31-46. Dorugade, A. V. and Kashid, D. N. (2010). Alternative method for choosing ridge parameter for regres- sion, International Journal of Applied Mathematical Sciences, 4(9), 447-456.
Gibbons, D. G. (1981). A simulation study of some ridge estimators,Journal of the American Statistical Association, 76, 131-139.
Gujarati, D.N.(1995). Basic Econometrics. McGraw-Hill, New York.
Hocking, R., Speed, F. M. and Lynn, M. J. (1976). A class of biased estimators in linear regression, Technometrics, 18(4), 425-437.
Hoerl, A.E. and Kennard, R.W. (1970). Ridge regression: biased estimation for non-orthogonal problems, Technometrics, 12, 55-67.
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. Lawless, J. F. and Wang, P. (1976). A simulation study of ridge and other regression estimators, Com- munications in Statistics A, 5, 307-323.
Lukman, A. F. and Ayinde, K. (2015). Review and classification of the Ridge Parameter Estimation
Techniques, Hacettepe Journal of Mathematics and Statistics, Accepted for Publication. Mansson, K., Shukur, G. and Kibria, B. M. G. (2010). A simulation study of some ridge regression estimators under different distributional assumptions,Communications in Statistics-Simulations and Com- putations, 39(8), 1639-1670.
McDonald, G. C. and Galarneau, D. I. (1975). A Monte Carlo evaluation of some ridge-type estimators,
Journal of the American Statistical Association, 70, 407-416. Muniz, G. and Kibria, B. M. G. (2009). On some ridge regression estimators: An empirical compari- son,Communications in Statistics-Simulation and Computation, 38, 621-630.
Muniz, G., Kibria, B.M.G., Mansson, K., Shukur, G. (2012). On Developing Ridge Regression Param- eters: A Graphical Investigation, SORT. 36(2), 115-138.
Nordberg, L. (1982). A procedure for determination of a good ridge parameter in linear regression,
Communications in Statistics A11, 285-309. Saleh, A. K. Md. E. and Kibria, B. M. G. (1993). Performances of some new preliminary test ridge regression estimators and their properties, Communications in Statistics-Theory and Methods, 22, 2747
Wichern, D. and Churchill, G. (1978). A Comparison of Ridge Estimators, Technometrics, 20, 301–311.
Year 2016,
Volume: 9 Issue: 3, 93 - 106, 01.09.2016
Alkhamisi, M., Khalaf, G. and Shukur, G. (2006). Some modifications for choosing ridge parameters,
Communications in Statistics- Theory and Methods, 35(11), 2005-2020.
Alkhamisi, M. and Shukur, G. (2007). A Monte Carlo study of recent ridge parameters, Commun. Statist.
Simulation and Computation, 36(3), 535-547. Dorugade, A. V. (2014). On comparison of some ridge parameters in Ridge Regression, Sri Lankan
Journal of Applied Statistics, 15(1), 31-46. Dorugade, A. V. and Kashid, D. N. (2010). Alternative method for choosing ridge parameter for regres- sion, International Journal of Applied Mathematical Sciences, 4(9), 447-456.
Gibbons, D. G. (1981). A simulation study of some ridge estimators,Journal of the American Statistical Association, 76, 131-139.
Gujarati, D.N.(1995). Basic Econometrics. McGraw-Hill, New York.
Hocking, R., Speed, F. M. and Lynn, M. J. (1976). A class of biased estimators in linear regression, Technometrics, 18(4), 425-437.
Hoerl, A.E. and Kennard, R.W. (1970). Ridge regression: biased estimation for non-orthogonal problems, Technometrics, 12, 55-67.
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. Lawless, J. F. and Wang, P. (1976). A simulation study of ridge and other regression estimators, Com- munications in Statistics A, 5, 307-323.
Lukman, A. F. and Ayinde, K. (2015). Review and classification of the Ridge Parameter Estimation
Techniques, Hacettepe Journal of Mathematics and Statistics, Accepted for Publication. Mansson, K., Shukur, G. and Kibria, B. M. G. (2010). A simulation study of some ridge regression estimators under different distributional assumptions,Communications in Statistics-Simulations and Com- putations, 39(8), 1639-1670.
McDonald, G. C. and Galarneau, D. I. (1975). A Monte Carlo evaluation of some ridge-type estimators,
Journal of the American Statistical Association, 70, 407-416. Muniz, G. and Kibria, B. M. G. (2009). On some ridge regression estimators: An empirical compari- son,Communications in Statistics-Simulation and Computation, 38, 621-630.
Muniz, G., Kibria, B.M.G., Mansson, K., Shukur, G. (2012). On Developing Ridge Regression Param- eters: A Graphical Investigation, SORT. 36(2), 115-138.
Nordberg, L. (1982). A procedure for determination of a good ridge parameter in linear regression,
Communications in Statistics A11, 285-309. Saleh, A. K. Md. E. and Kibria, B. M. G. (1993). Performances of some new preliminary test ridge regression estimators and their properties, Communications in Statistics-Theory and Methods, 22, 2747
Wichern, D. and Churchill, G. (1978). A Comparison of Ridge Estimators, Technometrics, 20, 301–311.
Lukman, A. F., & Ayinde., K. (2016). SOME IMPROVED CLASSIFICATION-BASED RIDGE PARAMETER OF HOERL AND KENNARD ESTIMATION TECHNIQUES. Istatistik Journal of The Turkish Statistical Association, 9(3), 93-106.
AMA
Lukman AF, Ayinde. K. SOME IMPROVED CLASSIFICATION-BASED RIDGE PARAMETER OF HOERL AND KENNARD ESTIMATION TECHNIQUES. IJTSA. September 2016;9(3):93-106.
Chicago
Lukman, Adewale F., and Kayode Ayinde. “SOME IMPROVED CLASSIFICATION-BASED RIDGE PARAMETER OF HOERL AND KENNARD ESTIMATION TECHNIQUES”. Istatistik Journal of The Turkish Statistical Association 9, no. 3 (September 2016): 93-106.
EndNote
Lukman AF, Ayinde. K (September 1, 2016) SOME IMPROVED CLASSIFICATION-BASED RIDGE PARAMETER OF HOERL AND KENNARD ESTIMATION TECHNIQUES. Istatistik Journal of The Turkish Statistical Association 9 3 93–106.
IEEE
A. F. Lukman and K. Ayinde., “SOME IMPROVED CLASSIFICATION-BASED RIDGE PARAMETER OF HOERL AND KENNARD ESTIMATION TECHNIQUES”, IJTSA, vol. 9, no. 3, pp. 93–106, 2016.
ISNAD
Lukman, Adewale F. - Ayinde., Kayode. “SOME IMPROVED CLASSIFICATION-BASED RIDGE PARAMETER OF HOERL AND KENNARD ESTIMATION TECHNIQUES”. Istatistik Journal of The Turkish Statistical Association 9/3 (September 2016), 93-106.
JAMA
Lukman AF, Ayinde. K. SOME IMPROVED CLASSIFICATION-BASED RIDGE PARAMETER OF HOERL AND KENNARD ESTIMATION TECHNIQUES. IJTSA. 2016;9:93–106.
MLA
Lukman, Adewale F. and Kayode Ayinde. “SOME IMPROVED CLASSIFICATION-BASED RIDGE PARAMETER OF HOERL AND KENNARD ESTIMATION TECHNIQUES”. Istatistik Journal of The Turkish Statistical Association, vol. 9, no. 3, 2016, pp. 93-106.
Vancouver
Lukman AF, Ayinde. K. SOME IMPROVED CLASSIFICATION-BASED RIDGE PARAMETER OF HOERL AND KENNARD ESTIMATION TECHNIQUES. IJTSA. 2016;9(3):93-106.