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

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  • C. A. Uzuke
  • J. I. Mbegbu

Abstract

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.

Suggested Citation

  • C. A. Uzuke & J. I. Mbegbu, 2016. "Graphical Investigation of Ridge Estimators When the Eigenvalues of the Matrix (X'X) are Skewed," International Journal of Sciences, Office ijSciences, vol. 5(03), pages 78-100, March.
    • Handle: RePEc:adm:journl:v:5:y:2016:i:3:p:78-100
    DOI: 10.18483/ijSci.972
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    References listed on IDEAS

    as
    1. John Zhang & Mahmud Ibrahim, 2005. "A simulation study on SPSS ridge regression and ordinary least squares regression procedures for multicollinearity data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(6), pages 571-588.
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