Exact distribution of Cook’s distance and identification of influential observations

Year 2015, Volume: 44 Issue: 1, 165 - 178, 01.02.2015

G.s. David Sam Jayakumar A. Sulthan

Abstract

This paper proposed the exact distribution of Cook’s distance used to
evaluate the influential observations in multiple linear regression analysis. The authors adopted the relationship proposed by Weisberg (1980),
Belsey et al. (1980) and showed the derived density function of the
cook’s distance in terms of the series expression form. Moreover, the
first two moments of the distribution are derived and the authors computed the critical points of Cook’s distance at $5\%$ and $1\%$ significance
level for different sample sizes based on no.of predictors. Finally, the numerical example shows the identification of the influential observations
and the results extracted from the proposed approach is more scientific,
systematic and it’s exactness outperforms the traditional rule of thumb
approach.

Keywords

Cook’s distance, influential observations, Series expression form, moments, critical points

References

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