Influence Diagnostics in Linear Regression Under Heteroscedasticity : A Different Approach

Abstract

Abtsrcat Many procedures are available to identify a single outlier or an isolated influential point in linear regression model. But the detection of multiple outliers or subset of influential points is rarely considered under heteroscedasticity and not been studied from the point of direct procedure. In this paper, dedinition and properties of an influence statistic for one or a set of observations in linear regression under heteroscedasticity is generalized. We express this influence statistic in terms of the residuals and the leverages.We prove that this statistic has asymptotically normal distribution and is able to detect a subset of high weighted leverage-outliers that will be undetected by Cook's distance. For illustration, a simulation study has been carried out and also a real data set has been analyzed.