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Performance of Some Modified Ordinary Ridge Regression Estimators

Satish Bhat


In multiple linear regressions, if the data suffer from severe multicollinearity, then the ordinary least squares (OLS) method become more sensitive to it, and in such a case OLS could yield wrong sign for some of the regression coefficients. Therefore, when such a situation arises, we could use one of the biased regression methods viz., ridge regression (RR), principal component regression(PCR), etc., as an alternative method to OLS. This paper pertains to ridge regression only. To overcome the problem of multicollinearity, here we propose some modified ordinary ridge estimators, which are defined by taking convex combinations of some of the existing estimators. Empirically performance of the suggested estimators is compared with some of the existing estimators which are considered in this study, and the results indicate the suggested estimators performed better in terms of MSE. Moreover, the suggested estimators are more robust to problem of linear dependency between the predictors.


Multiple linear regressions, multicollinearity, VIF, Ridge Parameter, MSE

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Horel, A. E. "Applications of ridge analysis toregression problems." Chem. Eng. Progress. 58 (1962): 54-59.

Hoerl, Arthur E., and Robert W. Kennard. "Ridge regression: applications to nonorthogonal problems." Technometrics 12.1 (1970): 69-82.

Hoerl, Arthur E., Robert W. Kannard, and Kent F. Baldwin. "Ridge regression: some simulations."Communications in Statistics-Theory and Methods 4.2 (1975): 105-123.

Halawa, A. M., and M. Y. El Bassiouni. "Tests of regression coefficients under ridge regression models." Journal of Statistical Computation and Simulation 65.1-4 (2000): 341-356.

Hastie, T., and R. Tibshirani. "Generalized Additive Models. Chapman Hall & CRC." Monographs on Statistics & Applied Probability. Chapman and Hall/CRC 1 (1990).

Alkhamisi, Mahdi A., and Ghazi Shukur. "A Monte Carlo study of recent ridge parameters." Communications in Statistics—Simulation and Computation® 36.3 (2007): 535-547.

Dorugade, A. V., and D. N. Kashid. "Alternative method for choosing ridge parameter for regression." Applied Mathematical Sciences 4.9 (2010): 447-456.

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

Kibria, BM Golam. "Performance of some new ridge regression estimators." Communications in Statistics-Simulation and Computation 32.2 (2003): 419-435.

Khalaf, Ghadban. "A proposed ridge parameter to improve the least square estimator." Journal of Modern Applied Statistical Methods 11.2 (2012): 15.


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