Statistical Methods & Applications

, Volume 19, Issue 3, pp 333–354 | Cite as

Infinitesimally Robust estimation in general smoothly parametrized models



The aim of the paper is to give a coherent account of the robustness approach based on shrinking neighborhoods in the case of i.i.d. observations, and add some theoretical complements. An important aspect of the approach is that it does not require any particular model structure but covers arbitrary parametric models if only smoothly parametrized. In the meantime, equal generality has been achieved by object-oriented implementation of the optimally robust estimators. Exponential families constitute the main examples in this article. Not pretending a complete data analysis, we evaluate the robust estimates on real datasets from literature by means of our R packages ROptEst and RobLox.


Exponential family Influence curves Asymptotically linear estimators Shrinking contamination, total variation, and Hellinger neighborhoods One-step construction Minmax MSE 

Mathematics Subject Classification (2000)

62-07 62F12 62F35 62G05 62G35 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Matthias Kohl
    • 1
  • Peter Ruckdeschel
    • 2
  • Helmut Rieder
    • 3
  1. 1.Jena University Hospital, Department of Anesthesiology and Intensive Care MedicineFriedrich-Schiller-University JenaJenaGermany
  2. 2.Fraunhofer-InstitutTechno-und WirtschaftsmathematikKaiserslauternGermany
  3. 3.Department of MathematicsUniversity of BayreuthBayreuthGermany

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