Assessing Influence on the Liu Estimates in Linear Regression Models

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...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2013-09, Vol.42 (17), p.3100-3116
Main Authors: Ullah, M. A., Pasha, G. R., Aslam, M.
Format: Article
Language:English
Subjects:
Approximation
Case deletion
Collinearity
Economic models
Estimates
Estimators
Heating
Least squares method
Leverage
Mathematical analysis
Mean shift outlier model
One-step approximation
Regression
Regression analysis
Statistics
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Summary: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.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2011.620206