B1110
Title: The concept of local robustness with a view toward statistical estimation and risk management
Authors: Volker Kraetschmer - University Duisburg-Essen (Germany) [presenting]
Alexander Schied - University of Mannheim (Germany)
Henryk Zaehle - Saarland University (Germany)
Abstract: Many standard estimators such as several maximum likelihood estimators or the empirical estimator for any law-invariant convex risk measure are not (qualitatively) robust in the classical sense. However, these estimators may nevertheless satisfy a local robustness property on relevant sets of distributions. After introducing this new concept, attention will be paid to identify sets of local robustness, and to explain the benefit of the knowledge of such sets. For instance, it will be be demonstrated that many maximum likelihood estimators are robust on their natural parametric domains. A second aim consists in extending the general theory of robust estimation to the local framework. In particular, a corresponding Hampel-type theorem is provided, linking local robustness of a plug-in estimator with a certain continuity condition.
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