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

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.