Exact distribution of Hadi's $(H^2)$ influence measure and identification of potential outliers

Abstract

This paper proposed an exact distribution of Hadi's influence measure that can be used to evaluate the potential outliers in a linear multiple regression analysis. The authors explored a relationship between the measure in terms of two independent F-ratios and they derived density function of the measure in a complicated series expression form with Gauss hyper-geometric function. Moreover, the first two moments of the distribution are derived in terms of Beta function and the authors computed the critical points of Hadi's measures at 5% and 1% significance level for different sample sizes and varying no. of predictors. Finally, the numerical example shows the identification of the potential outliers and the results extracted from the proposed approaches are more scientific, systematic and its exactness outperforms the Hadi's traditional approach.

Keywords

• Hadi's measure,Potential outliers,Series expression form,Gauss hyper-geometric function,Moments,Beta function,Critical points

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