Graphical Investigation of Ridge Estimators When the Eigenvalues of the Matrix (X'X) are Skewed

Graphical Investigation of Ridge Estimators When the Eigenvalues of the Matrix (X'X) are Skewed

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Author(s): C. A. Uzuke, J. I. Mbegbu

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DOI: 10.18483/ijSci.972 243 707 78-100 Volume 5 - Mar 2016


Methods of estimating the ridge parameter in ridge regression analysis are available in the literature. This paper proposed some methods based on the works of Lawless and Wang (1976) and Khalaf and Shurkur (2005). A simulation study was conducted and mean square error (MSE) criterion was used to compare the performances of the proposed estimators and some other existing ones. It was observed that the performance of the these estimators depend on the variance of the random error , the correlation among the explanatory variables , the sample size and the number of explanatory variables . The increase in the number of explanatory variables and increase in the sample size reduces the MSE of the estimators even when the correlation between the explanatory variables are high, but for small sample size, MSE increases as the values of increases. One of the proposed methods outperforms all the other existing and proposed methods considered in terms of MSE values.


Eigenvalues, Mean Square Error, Multicollinearity, Ridge regression, Skewness.


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