WSEAS Transactions on Mathematics


Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 17, 2018


Some Improved Generalized Ridge Estimators and their Comparison

AUTHORS: A. F. Lukman, A. Haadi, K. Ayinde, C. A. Onate, B. Gbadamosi, N. Oladejo Nathaniel

Download as PDF

The problem of multicollinearity is often encountered in time series data since explanatory variables included in the model often share a common trend. Various methods exist in literatures to handle this problem. Among them is the most widely used ridge regression estimator which depends on the ridge parameter. This estimator can be subdivided into either generalized ridge or ordinary ridge estimators. Variance inflation factor is introduced to replace eigenvalue in the generalized ridge estimator proposed by Lawless and Wang (1976). Through this modification some new generalized ridge parameters are proposed and investigated via simulation study. The performances of these proposed estimators are compared with the existing ones using mean square error. Results show that the proposed estimators perform better than the existing ones. It is evident that increasing the level of multicollinearity and number of regressors has positive effect on the MSE. Also, the performance of the estimators depends on the level of error variances.

KEYWORDS: Multicollinearity, Generalized ridge, Ordinary ridge, Simulation study

REFERENCES:

[1] K. Adnan, A. Yasin, and G. Asir. 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, 20, 2016, 89-99.

[2] F. Batah, T. Ramanathan and S. Gore. The Efficiency of Modified Jackknife and Ridge Type Regression Estimators: A Comparison, Surveys in Mathematics and its Applications, 24(2), 2008, F.157 – 174.

[3] A.P. Dempster, M. Schatzoff and N. Wermuth. A simulation study of alternatives to Ordinary Least Squares. Journal of the American Statistical Association, 72, 1977, 77-91.

[4] A. V. Dorugade. New ridge parameters for ridge regression. Journal of the Association of Arab Universities for Basic and Applied Sciences, 15, 2014, 94-99.

[5] L. Firinguetti. A generalized ridge regression estimator and its finite sample properties. Communicaition in StatisticsTheory and Methods, 28(5), 1999, 1217- 1229.

[6] A.E. Hoerl and R.W. Kennard. Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12, 1970, 55-67.

[7] A. E. Hoerl, R.W. Kennard and K. F. Baldwin. Ridge regression: Some simulation. Communications in Statistics, 4 (2), 1975, 105–123.

[8] G. Khalaf and G. Shukur. Choosing ridge parameters for regression problems. Communications in Statistics - Theory and Methods, 34, 1988, 1177-1182.

[9] G. Khalaf and M. Iguernane. Multicollinearity and a Ridge Parameter Estimation Approach. Journal of Modern Applied Statistical Methods, 15(2), 2016, 400-410.

[10] B. M. G. Kibria. Performance of some new ridge regression estimators. Communications in Statistics - Simulation and Computation, 32, 2003, 419- 435.

[11] B. M. G. Kibria and B. Shipra. Some Ridge Regression Estimators and Their Performances. Journal of Modern Applied Statistical Methods, 15(1), 2016, 206-231.

[12] J. F. Lawless and P. Wang. A simulation study of ridge and other regression estimators. Communications in Statistics A, 5, 1976, 307-323.

[13] A. F. Lukman and K. Ayinde. Some Improved Classification-Based Ridge Parameter of Hoerl and Kennard Estimation Techniques. Istatistik, Journal of the Turkish Statistical Association, 9(3), 2016, 93-106.

[14] A. F. Lukman and K. Ayinde. Review and classification of the Ridge Parameter Estimation Techniques. Hacettepe Journal of Mathematics and Statistics, 46(5), 2017, 953-967.

[15] A. F. Lukman and O. T. Arowolo. Newly Proposed Biased Ridge Estimator: An Application to the Nigerian Economy. Pakistan Journal of Statistics, 34(2), 2018, 91-98.

[16] A. F. Lukman, K. Ayinde, A. O. Okunola, O. B. Akanbi and C. A. Onate. Classification-Based Ridge Estimation Techniques of Alkhamisi Methods. Journal of Probability and Statistical Sciences. 16(2), 2018, 165-181.

[17] G. C. McDonald and D. I. Galarneau. A Monte Carlo evaluation of some ridge-type estimators. Journal of the American Statistical Association, 70, 1975, 407-416.

[18] Muniz, G. and Kibria, B. M. G. (2009). On some ridge regression estimators: An empirical comparison. Communications in Statistics-Simulation and Computation, 38, 2005, 621-630.

[19] M. Nomura. On the almost unbiased ridge regression estimator. Communications in Statistics–Simulation and Computation 17, 729–743.

[20] C. G. Troskie and D. O. Chalton. A bayesian estimate for the constants in ridge regression. South African Statistical Journal, 30, 1996, 119-137.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #45, pp. 369-376


Copyright Β© 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

Bulletin Board

Currently:

The editorial board is accepting papers.


WSEAS Main Site