Assessing Influence on the Liu Estimates in Linear Regression Models

Abstract

The Liu estimator has been developed as an alternative to the ordinary least squares estimator in the presence of collinearity among the elements of regressors in linear regression models. We present the DFFITS and different versions of the Cook distance analogous to the ones given for the ordinary linear regression models of each individual observation on the Liu estimates. We suggest a version of the Cook distance based on one-step approximation. The mean shift outlier model for the Liu regression has also been investigated. Moreover, using the Sherman-Morrison-Woodbury theorem, we find approximate versions of the DFFITS and the Cook distance. The proposed diagnostics are evaluated on two data sets and yield promising results.

Keywords:

• Case deletion
• Collinearity
• Leverage
• Mean shift outlier model
• One-step approximation

Mathematics Subject Classification:

• 62J20
• 62J12

Acknowledgment

The authors are very grateful to the Associate Editor and the anonymous referees for their valuable comments on the earlier versions of this article.

Notes

Values with + suggest the cases with the values more than the cutoff point.

Values with + suggest the cases with the values more than the cutoff point.