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Abstract
The detection of outliers and influential observations has received a great deal of attention in the statistical literature in the context of least-squares (LS) regression. However, the explanatory variables can be correlated with each other and alternatives to LS come out to address outliers/influential observations and multicollinearity, simultaneously. This paper proposes new influence measures based on the affine combination type regression for the detection of influential observations in the linear regression model when multicollinearity exists. Approximate influence measures are also proposed for the affine combination type regression. Since the affine combination type regression includes the ridge, the Liu and the shrunken regressions as special cases, influence measures under the ridge, the Liu and the shrunken regressions are also examined to see the possible effect that multicollinearity can have on the influence of an observation. The Longley data set is given illustrating the influence measures in affine combination type regression and also in ridge, Liu and shrunken regressions so that the performance of different biased regressions on detecting and assessing the influential observations is examined.
Acknowledgements
The author expresses her gratitude to the unknown referees for their valuable comments.
Notes
Appendix 1 is not given in the paper to save space and it is available as electronic supplementary material.
Appendix 2 is not given in the paper to save space and it is available as electronic supplementary material.
The derivation of EquationEquation (17) is given in Appendix 3 which is available as electronic supplementary material.
Appendix 4 is not given in the paper to save space and it is available as electronic supplementary material.