TWO NEW RIDGE PARAMETERS AND A GUIDE FOR SELECTING AN APPROPRIATE RIDGE PARAMETER IN LINEAR REGRESSION

Year 2016, Volume: 29 Issue: 1, 201 - 211, 21.03.2016

Atila Göktaş Volkan Sevinç

Abstract

The ridge regression estimator was first introduced by Hoerl and Kennard [6] as an alternative method to the ordinary least squares (OLS) estimator when multicollinearity exists among regressors. Ridge regression depends on the estimation of the ridge parameter presented in this study as k. On the other hand there is not a standard way of determining k. In the literature, there are a lot of proposed ridge parameters.

The aim of this paper is to introduce two new ridge parameters and make comparison of 37 different ridge parameters including the proposed ones. A simulation study has been conducted to make comparisons in terms of the mean square error criterion. It is found that the proposed ridge parameters produce better results than most of the other parameters. The parameters proposed by Asar et. al. [2] very recently did not perform as well as their results. In fact the parameters we have proposed did perform much better than theirs in every single case. However there is no explicit ridge parameter that performs well in every situation. The ridge estimators act differently in various sample sizes, dimensions and collinearity degrees. We think that this study is helpful for researchers employing ridge regression as they may use the comparative results provided in the study to make a decision of choosing the best ridge parameter for their case.

Keywords

Ridge regression, ridge parameters, collinear data generation

References

• REFERENCES
• Alkhamisi, M. A. and G. Shukur. 'A Monte Carlo Study Of Recent Ridge Parameters'. Communications in Statistics - Simulation and Computation 36.3 (2007).
• Asar, Y., Karaibrahimoğlu, A. and Genç, A. 'Modified Ridge Regression Parameters: A Comparative Monte Carlo Study'. Hacettepe Journal of Mathematics and Statistics 43 (5) (2014).
• Batah, F. S., Ramnathan, T. and Gore, S. D. 'The Efficiency Of Modified Jackknife And Ridge Type Regression Estimators: A Comparison. 24 (2) (2008).
• Dorugade, A. V. 'New Ridge Parameters For Ridge Regression'. Journal of the Association of Arab Universities for Basic and Applied Sciences 15 (2014).
• Hoerl, A. E., Kennard, R. and Baldwin, K. 'Ridge Regression: Some Simulations'. Comm. in Stats. - Simulation & Comp. 4.2 (1975).
• Hoerl, A. E. and Kennard, R. 'Ridge Regression: Biased Estimation For Nonorthogonal Problems'. Technometrics 12.1 (1970a).
• Hoerl, A.E. and Kennard, R. 'Ridge Regression: Applications To Nonorthogonal Problems'. Technometrics 12.1 (1970b).
• Karaibrahimoğlu A., Asar Y. and Genç A., 'Some new modifications of Kibria’s and Dorugade’s methods: An application to Turkish GDP data', Journal of the Association of Arab Universities for Basic and Applied Sciences, Available online 7 October 2014, ISSN 1815-3852,http://dx.doi.org/10.1016/j.jaubas.2014.08.005.
• Khalaf, G. and Shukur, G. 'Choosing Ridge Parameter For Regression Problems'. Communications in Statistics - Theory and Methods 34.5 (2005).
• Kibria, G. 'Performance Of Some New Ridge Regression Estimators'. Communications in Statistics - Simulation and Computation 32.2 (2003).
• Kibria, G., Månsson, K. and Shukur, G. 'Performance Of Some Logistic Ridge Regression Estimators'. Comput Econ 40.4 (2011).
• Lawless, J. and Wang, P. 'A Simulation Study Of Ridge And Other Regression Estimators'. Comm. in Stats. - Theory & Methods 5.4 (1976).
• Mansson K., Shukur G. and Kibria G. 'On Some Ridge Regression Estimators: A Monte Carlo Simulation Study Under Different Error Variances', Journal of Statistics, 17, 1-22, (2010).
• Muniz, G. and Kibria, G. 'On Some Ridge Regression Estimators: An Empirical Comparisons'. Communications in Statistics - Simulation and Computation 38.3 (2009).
• Nomura, M. 'On The Almost Unbiased Ridge Regression Estimator'. Communications in Statistics - Simulation and Computation 17.3 (1988).
• Norliza, A., Maizah, H. A. and Robin, A. 'A Comparative Study On Some Methods For Handling Multicollinearity Problems'. Mathematika 22 (2) (2006).
• Sakallioglu S. and Kaciranlar S. 'A new biased estimator based on ridge estimation', Stat
• Papers, 49, 669-689, (2008).
• Saleh, A.K. and Kibria, B.M. 'Performances of some new preliminary test ridge regression estimators and their properties', Communications in Statistics - Theory and Methods, 22, 2747-2764, (1993).
• Schaeffer, R.L., Roi, L.D. and Wolfe, R. A. 'A Ridge Logistic Estimator'. Communications in Statistics - Theory and Methods 13.1 (1984).