IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v143y2016icp12-31.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X15001888
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2015.08.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hable, Robert & Christmann, Andreas, 2011. "On qualitative robustness of support vector machines," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 993-1007, July.
    2. 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.
    3. 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.
    4. 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.
    5. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Post-Print hal-00413729, HAL.
    6. Volker Kratschmer & Alexander Schied & Henryk Zahle, 2012. "Comparative and qualitative robustness for law-invariant risk measures," Papers 1204.2458, arXiv.org, revised Jan 2014.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Krätschmer, Volker & Schied, Alexander & Zähle, Henryk, 2017. "Domains of weak continuity of statistical functionals with a view toward robust statistics," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 1-19.
    2. Krätschmer Volker & Schied Alexander & Zähle Henryk, 2015. "Quasi-Hadamard differentiability of general risk functionals and its application," Statistics & Risk Modeling, De Gruyter, vol. 32(1), pages 25-47, April.
    3. M. Burzoni & I. Peri & C. M. Ruffo, 2017. "On the properties of the Lambda value at risk: robustness, elicitability and consistency," Quantitative Finance, Taylor & Francis Journals, vol. 17(11), pages 1735-1743, November.
    4. Ruodu Wang & Johanna F. Ziegel, 2014. "Distortion Risk Measures and Elicitability," Papers 1405.3769, arXiv.org, revised May 2014.
    5. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Ruodu Wang, 2017. "Risk bounds for factor models," Finance and Stochastics, Springer, vol. 21(3), pages 631-659, July.
    6. Lazar, Emese & Zhang, Ning, 2019. "Model risk of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 74-93.
    7. Fissler Tobias & Ziegel Johanna F., 2021. "On the elicitability of range value at risk," Statistics & Risk Modeling, De Gruyter, vol. 38(1-2), pages 25-46, January.
    8. Koch-Medina Pablo & Munari Cosimo, 2014. "Law-invariant risk measures: Extension properties and qualitative robustness," Statistics & Risk Modeling, De Gruyter, vol. 31(3-4), pages 215-236, December.
    9. Tobias Fissler & Johanna F. Ziegel, 2015. "Higher order elicitability and Osband's principle," Papers 1503.08123, arXiv.org, revised Sep 2015.
    10. Matteo Burzoni & Ilaria Peri & Chiara Maria Ruffo, 2016. "On the properties of the Lambda value at risk: robustness, elicitability and consistency," Papers 1603.09491, arXiv.org, revised Feb 2017.
    11. Asimit, Alexandru V. & Bignozzi, Valeria & Cheung, Ka Chun & Hu, Junlei & Kim, Eun-Seok, 2017. "Robust and Pareto optimality of insurance contracts," European Journal of Operational Research, Elsevier, vol. 262(2), pages 720-732.
    12. Jiang, Jie & Peng, Shen, 2024. "Mathematical programs with distributionally robust chance constraints: Statistical robustness, discretization and reformulation," European Journal of Operational Research, Elsevier, vol. 313(2), pages 616-627.
    13. Kim, Sojung & Weber, Stefan, 2022. "Simulation methods for robust risk assessment and the distorted mix approach," European Journal of Operational Research, Elsevier, vol. 298(1), pages 380-398.
    14. Marcelo Brutti Righi & Marlon Ruoso Moresco, 2024. "Inf-convolution and optimal risk sharing with countable sets of risk measures," Annals of Operations Research, Springer, vol. 336(1), pages 829-860, May.
    15. Ruodu Wang, 2016. "Regulatory arbitrage of risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 337-347, March.
    16. Righi, Marcelo Brutti & Müller, Fernanda Maria & Moresco, Marlon Ruoso, 2020. "On a robust risk measurement approach for capital determination errors minimization," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 199-211.
    17. Burzoni, Matteo & Munari, Cosimo & Wang, Ruodu, 2022. "Adjusted Expected Shortfall," Journal of Banking & Finance, Elsevier, vol. 134(C).
    18. Sally G. Arcidiacono & Damiano Rossello, 2022. "A hybrid approach to the discrepancy in financial performance’s robustness," Operational Research, Springer, vol. 22(5), pages 5441-5476, November.
    19. Mathieu Cambou & Damir Filipović, 2018. "Replicating portfolio approach to capital calculation," Finance and Stochastics, Springer, vol. 22(1), pages 181-203, January.
    20. Xue Dong He & Xianhua Peng, 2017. "Surplus-Invariant, Law-Invariant, and Conic Acceptance Sets Must be the Sets Induced by Value-at-Risk," Papers 1707.05596, arXiv.org, revised Jan 2018.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:12-31. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.