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Assessing Influence on the Liu Estimates in Linear Regression Models
Authors:M A Ullah  G R Pasha  M Aslam
Institution:1. Department of Statistics , Bahauddin Zakariya University , Multan , Pakistan aman_stat@yahoo.com;3. Sub Campus , D. G. Khan Bahauddin Zakariya University , Multan , Pakistan;4. Department of Statistics , Bahauddin Zakariya University , Multan , Pakistan
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
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