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New Modification of Robust Ridge Regression Estimator |
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PP: 1575-1588 |
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doi:10.18576/jsap/130602
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Author(s) |
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Ehab A. Mahmood,
E. Falih Fadel,
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Abstract |
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| Multicollinearity problem occurs in the multiple linear regression model when an independent variable is correlated with one or more of the other independent variables. This problem breaks the assumption of the ordinary least squares OLS method, so in this case we cannot use it to estimate the model coefficients. The ridge regression method is an alternative method used to deal with the multicollinearity problem to estimate parameters of the multiple linear regression model. However, this method causes misleading inferences when the data have leverage points. So, many robust methods have been proposed to deal with the multicollinearity problem and leverage points. Unfortunately, to date this problem still exists and researchers try to propose new estimators. This motivated us to propose a robust method to estimate the parameters of the multiple linear regression model to deal with leverage points and multicollinearity problems simultaneously. In this paper, we propose new modification of three formulas of ridge parameter (k) based on MM-estimator. The performance is evaluated with some other available estimators using the bias and the mean square error MSE criteria. Simulation results show that the robust proposed estimators outperform other considered estimators. Moreover, the ridgemed-MM is the best estimator at different percentages of leverage points and degree of correlation. Finally, the results of real-life examples show that the ridgemed-MM is the best estimator among the other considered estimators. |
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