A NON-STUDENT DISTRIBUTION OF JACK-KNIFE RESIDUALS AND IDENTIFICATION OF OUTLIERS
Keywords:
Jack Knife Residuals, External Studentized Residual, Outliers, T-Ratio, F- Ratio, Moments, Critical Points.Abstract
This paper proposes the exact distribution of Jack-Knife residual which is formally called as external studentized residual and used to evaluate the outliers in linear multiple regression analysis. The authors have proved that the Jackknife residuals do not follow student’s t-distribution and they have explored the relationship among Jack-Knife residual, t-ratio and F- ratio and have expressed the derived density function of the residual in terms of series expression form. Moreover, the new form of the distribution is symmetric, first two moments of the distribution are derived and the authors have computed the critical points of Jack Knife residual at 5% and 1% level of significance and for varying sample sizes and predictors. Finally, the numerical example shows that the results extracted from the proposed approach and classical approach are similar even though the proposed distribution of the Jackknife residuals is different.
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