A Diagnostic Measure for Influential Observations in Linear Regression

Abstract

In linear regression it is a common practice of measuring influence of an observation is to delete the case from the analysis and to investigate the change in the parameters or in the vector of forecasts resulting from this deletion. Pena (2005) introduced a new idea to measure the influence of an observation based on how this observation is being influenced by the rest of the data. In this article we propose a new influence measure extending the idea of Pena to group deletion for identifying multiple influential observations in linear regression. We investigate the usefulness of the proposed technique by two well-referred data sets, an artificial large data with high-dimension and heterogeneous sample points and by reporting a Monte Carlo simulation experiment.

Keywords:

• Group deletion
• High leverage point
• Masking
• Outlier
• Swamping

Mathematics Subject Classification:

• 62J05
• 62J20

Acknowledgments

The authors gratefully thank the Editor and anonymous reviewer for their helpful comments and suggestions that substantially improve this present version of the article.