On The Exact Distribution of Andrew-Pregibon (AP) Statistic and Identification of Influential Observations

Abstract

This paper proposed the exact distribution of Andrew-pregibon -statistic used to evaluate the influential observations in linear multiple regression analysis. The authors explored the relationship between the AP-statistic in terms of two independent F-ratio’s and they show the derived density function of the statistic in a series expression form and also extended the work of steece (1976) to show the density function of AP-statistic in terms of Gauss hyper-geometric function as an alternative form. Moreover, the first two moments of the distribution are derived and the authors computed the critical points of AP-statistic at 5% and 1% significance level for different sample sizes and varying no.of predictors. Finally, the numerical example shows the identification of the influential observations and the results extracted from the proposed approaches are more scientific, systematic and it’s exactness outperforms the traditional Andrew-pregibon’s approach.