The mean-shift outlier model in general weighted regression and its applications

Abstract

Consider the general weighted linear regression model y=Xβ+ε, where E(ε)=0,Cov(ε)=Vσ 2,σ 2 is an unknown positive scalar, and V is a symmetric positive-definite matrix not necessary diagonal. Two models, the mean-shift outlier model and the case-deletion model, can be employed to develop multiple case-deletion diagnostics for the linear model. The multiple case-deletion diagnostics are obtained via the mean-shift outlier model in this article and are shown to be equivalent to the deletion diagnostics via the case deletion model obtained by Preisser and Qaqish (1996, Biometrika, 83, 551-562). In addition, computing the multiple case-deletion diagnostics obtained via the mean-shift outlier model is faster than computing the one based on the more commonly used case-deletion model in some situations. Applications of the multiple deletion diagnostics developed from the mean-shift outlier model are also given for regression analysis with the likelihood function available and regression analysis based on generalized estimating equations. These applications include survival models and the generalized estimating equations of Liang and Zeger (1986, Biometrika, 73, 13-22). Several numerical experiments as well as a real example are given as illustrations. © 1999 Elsevier Science B.V.