A note on the use of residuals for detecting an outlier in linear regression

Abstract

SUMMARY Consider the usual linear regression model y = Xβ +ε, where the vector ε has E (ε) = 0, cov (ε) = σ 2 V , where V is known. Let e = y-ŷ be the least squares residual vector. It is shown that a test based on the transformed residual vector d * = V −1 e has, in the class of linear transformations of e , certain optimal power properties for detecting the presence of a single outlier when the label of the outlier observation is unknown. The outlier model considered here is that of shift in location.