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

Consider the usual linear regression model y = XfB + e, where the vector E has E(e) = 0, COV (E) = U2 V, where V is known. Let e = y-y be the least squares residual vector. It is shown that a test based on the transformed residual vector d* = V' 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.