A note on some new modifications of ridge estimators

Yasin Asar, Aşır Genç

Abstract


Ridge estimator is an alternative to ordinary least square estimator when there is multicollinearity problem. There are many proposed estimators in literature. In this paper, we propose new estimators which are modifications of the estimator suggested by Lawless and Wang (1976). A Monte Carlo experiment has been conducted for the comparison of the performances of the estimators. Mean squared error (MSE) is used as a performance criterion. The benefits of new estimators are illustrated using two real datasets. According to both simulation results and applications, our new estimators have better performances in the sense of MSE in most of the situations.


Keywords


Monte Carlo simulation; MSE; multicollinearity; OLS; ridge estimator; ridge regression

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References


Alkhamisi, M. A., Khalaf, G., and Shukur, G. (2006). Some modifications for choosing ridge parameters. Communications in Statistics—Theory and Methods, 35(11), 2005-2020.

Alkhamisi, M. A., and Shukur, G. (2007). A Monte Carlo study of recent ridge parameters. Communications in Statistics—Simulation and Computation®, 36(3), 535-547.

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

Gruber, M. (1998). Improving Efficiency by Shrinkage: The James--Stein and Ridge Regression Estimators (Vol. 156): CRC Press.

Hoerl, A. E., and Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67.

Hoerl, A. E., Kennard, R. W., and Baldwin, K. F. (1975). Ridge regression: some simulations. Communications in Statistics-Theory and Methods, 4(2), 105-123.

Kaçıranlar, S., and Sakallıoğlu, S. (2001). Combining the Liu estimator and the principal component regression estimator. Communications in Statistics - Theory and Methods, 30(12), 2699-2705.

Khalaf, G., and Shukur, G. (2005). Choosing ridge parameter for regression problems. Communications in Statistics - Theory and Methods, 34(5), 1177-1182.

Kibria, B. M. G. (2003). Performance of some new ridge regression estimators. Communications in Statistics-Simulation and Computation, 32(2), 419-435.

Lawless, J. F., and Wang, P. (1976). A simulation study of ridge and other regression estimators. Communications in Statistics-Theory and Methods, 5(4).

Mansson, K., Shukur, G., and Kibria, B. G. (2010). On some ridge regression estimators: A Monte Carlo simulation study under different error variances. Journal of Statistics, 17(1), 1-22.

Muniz, G., and Kibria, B. G. (2009). On some ridge regression estimators: An empirical comparisons. Communications in Statistics—Simulation and Computation®, 38(3), 621-630.

Muniz, G., Kibria, B. G., Mansson, K., and Shukur, G. (2012). On developing ridge regression parameters: a graphical investigation. Sort: Statistics and Operations Research Transactions, 36(2), 115-138.

Newhouse, J. P., and Oman, S. D. (1971). An evaluation of ridge estimators. PR. RAND CORP SANTA MONICA CALIF, 716.

Saleh, A. M., and Kibria, B. M. G. (1993). Performance of some new preliminary test ridge regression estimators and their properties. Communications in Statistics-Theory and Methods, 22(10), 2747-2764.

Trenkler, G. (1978). An iteration estimator for the linear model COMP-STAT 1978 (Proc. Third Sympos. Comput. Statist., Leiden, 1978) (pp. 125-131): Physika Vienna.


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