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Infinitesimally robust estimation in general smoothly parametrized models. (English) Zbl 1333.62095
Summary: 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.

MSC:
62F35 Robustness and adaptive procedures (parametric inference)
62G05 Nonparametric estimation
62F12 Asymptotic properties of parametric estimators
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