On using the distribution of Cook-Weisberg statistic and identification of influential observations

Abstract

This paper proposed the distribution of Cook-Weisberg statistic used toevaluate the inuential observations in linear multiple regression analysis.The authors explored the relationship between the CW statistic and COVratio (Co-variance ratio) in terms of two independent F-ratio's and they showthe derived density function of the measure in a series expression form. More-over, the rst two moments of the distribution are derived in terms of Beta,di-gamma, poly-gamma functions, upper control limit of CW-statistic is alsoestablished and the authors computed the critical points of CW-statistic at5% and 1% signicance level for dierent sample sizes and varying no.ofpredictors. Finally, the numerical example shows the identication of the influential observations and the results extracted from the proposed approachesare more scientic, systematic and it's exactness outperforms the traditionalapproach.