Advances and Applications in Statistics
Volume 62, Issue 1, Pages 97 - 105
(May 2020) http://dx.doi.org/10.17654/AS062010097 |
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A MONTE CARLO COMPARISON BETWEEN LEAST SQUARES AND THE NEW RIDGE REGRESSION PARAMETERS
Mowafaq Muhammed Al-Kassab and Mohammed Qasim Al-Awjar
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Abstract: The correlation (or multicollinearity) between the explanatory variables in multiple linear regression raises the variances of the least squares estimators. These estimators become unstable and may have wrong signs. Therefore, we resort to biased regression methods. The new ridge regression parameter method introduced by Al-Kassab and Al-Awjar [4] is used to estimate the regression parameters. A Monte Carlo method is used to estimate these regression parameters and a comparison between the ordinary least squares and the new ridge regression parameter methods was made in the sense of having smaller mean squares error. Based on simulation study, we found that the new ridge regression method where the ridge parameter k is a vector performs better than the ordinary least squares method. |
Keywords and phrases: multicollinearity, least squares, ridge parameters, matrix, mean squares error, simulation study.
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