Before revision:  These optimally-robust estimators are compared to maximum likelihood, skipped maximum likelihood, Cramer-von-Mises minimum distance, method of median, and Pickands estimators. To quantify their deviation from robust optimality, for each of these suboptimal estimators, we determine the finite sample breakdown point, the influence function, as well as the statistical accuracy measured by asymptotic bias, variance, and MSE - all evaluated uniformly on shrinking neighborhoods. These asymptotic findings are complemented by an extensive simulation study to assess their finite sample behavior .
After revision:  These optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calculation of the regulatory capital required by Basel II for a bank to cover operational risk. In this context the tail behavior of the underlying distribution is crucial. This is where extreme value theory enters, suggesting to estimate these high quantiles parameterically using, e.g. GPDs. Robust statistics in this context offers procedures bounding the influence of single observations, so provides reliable inference in the presence of moderate deviations from the distributional model assumptions, respectively from the mechanisms underlying the PBHT .