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A definition of qualitative robustness for general point estimators, and examples

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  • Zähle, Henryk

Abstract

A definition of qualitative robustness for point estimators in general statistical models is proposed. Some criteria for robustness are established and applied to estimators in parametric, semiparametric, and nonparametric models. In specific nonparametric models, the proposed definition boils down to Hampel robustness. It is also explained how plug-in estimators in certain nonparametric models can be reasonably classified w.r.t. their degrees of robustness.

Suggested Citation

  • Zähle, Henryk, 2016. "A definition of qualitative robustness for general point estimators, and examples," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 12-31.
    • Handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:12-31
    DOI: 10.1016/j.jmva.2015.08.004
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    References listed on IDEAS

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    1. Volker Krätschmer & Alexander Schied & Henryk Zähle, 2014. "Comparative and qualitative robustness for law-invariant risk measures," Finance and Stochastics, Springer, vol. 18(2), pages 271-295, April.
    2. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Post-Print hal-00413729, HAL.
    3. Volker Kratschmer & Alexander Schied & Henryk Zahle, 2012. "Comparative and qualitative robustness for law-invariant risk measures," Papers 1204.2458, arXiv.org, revised Jan 2014.
    4. Hable, Robert & Christmann, Andreas, 2011. "On qualitative robustness of support vector machines," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 993-1007, July.
    5. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 593-606.
    6. Krätschmer, Volker & Schied, Alexander & Zähle, Henryk, 2012. "Qualitative and infinitesimal robustness of tail-dependent statistical functionals," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 35-47, January.
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