The maximum asymptotic bias of outlier identifiers

In their paper, Davies and Gather (1993) formalized the task of outlier identification, considering also certain performance criteria for outlier identifiers. One of those Criteria, the maximum asymptotic bias, is carried over here to multivariate outlier identifiers. We show how this term depends on the respective biases of estimators which are used to construct the identifier. It turns out that the use of high breakdown robust estimators is not sufficient to achieve outlier identifiers with bounded maximum asymptotic bias.