IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v65y2003i1p81-94.html

Comprehensive definitions of breakdown points for independent and dependent observations

Author

Listed:
  • Marc G. Genton
  • André Lucas

Abstract

Summary. We provide a new definition of breakdown in finite samples, with an extension to asymptotic breakdown. Previous definitions centre on defining a critical region for either the parameter or the objective function. If for a particular outlier configuration the critical region is entered, breakdown is said to occur. In contrast with the traditional approach, we leave the definition of the critical region implicit. Our proposal encompasses previous definitions of breakdown in linear and non‐linear regression settings. In some cases, it leads to a different and more intuitive notion of breakdown than other procedures that are available. An important advantage of our new definition is that it also applies to models for dependent observations where current definitions of breakdown typically fail. We illustrate our suggestion by using examples from linear and non‐linear regression, and time series.

Suggested Citation

  • Marc G. Genton & André Lucas, 2003. "Comprehensive definitions of breakdown points for independent and dependent observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 81-94, February.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:1:p:81-94
    DOI: 10.1111/1467-9868.00373
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9868.00373
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9868.00373?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
    ---><---

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cizek, P., 2005. "Trimmed Likelihood-based Estimation in Binary Regression Models," Discussion Paper 2005-108, Tilburg University, Center for Economic Research.
    2. Cizek, Pavel, 2008. "Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 687-696, June.
    3. Cizek, P., 2007. "General Trimmed Estimation : Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaces DP 2007-1)," Other publications TiSEM eeccf622-dd18-41d4-a2f9-b, Tilburg University, School of Economics and Management.
    4. P. Čížek & M. Aquaro, 2018. "Robust estimation and moment selection in dynamic fixed-effects panel data models," Computational Statistics, Springer, vol. 33(2), pages 675-708, June.
    5. Vicky Fasen‐Hartmann & Sebastian Kimmig, 2020. "Robust estimation of stationary continuous‐time arma models via indirect inference," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 620-651, September.
    6. Luke A. Prendergast & Robert G. Staudte, 2017. "When large n is not enough – Distribution-free interval estimators for ratios of quantiles," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(3), pages 277-293, September.
    7. Alessio Farcomeni & Luca Greco, 2015. "S-estimation of hidden Markov models," Computational Statistics, Springer, vol. 30(1), pages 57-80, March.
    8. Cizek, P., 2009. "Generalized Methods of Trimmed Moments," Discussion Paper 2009-25, Tilburg University, Center for Economic Research.
    9. Pavel Čížek, 2013. "Reweighted least trimmed squares: an alternative to one-step estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 514-533, September.
    10. Cízek, Pavel, 2011. "Semiparametrically weighted robust estimation of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 774-788, January.
    11. Čížek, Pavel, 2012. "Semiparametric robust estimation of truncated and censored regression models," Journal of Econometrics, Elsevier, vol. 168(2), pages 347-366.
    12. Daniel Kosiorowski, 2015. "Two procedures for robust monitoring of probability distributions of economic data stream induced by depth functions," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 25(1), pages 55-79.
    13. repec:hum:wpaper:sfb649dp2006-050 is not listed on IDEAS
    14. Čίžek, Pavel & Härdle, Wolfgang Karl, 2006. "Robust econometrics," SFB 649 Discussion Papers 2006-050, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Jaakko Nevalainen & Denis Larocque & Hannu Oja, 2007. "A weighted spatial median for clustered data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 355-379, February.
    16. Cizek, P., 2007. "Efficient Robust Estimation of Time-Series Regression Models," Discussion Paper 2007-95, Tilburg University, Center for Economic Research.
    17. Genton, Mark G. & Ruiz-Gazen, Anne, 2009. "Visualizing Influential Observations in Dependent Data," TSE Working Papers 09-051, Toulouse School of Economics (TSE).
    18. Aquaro, M. & Čížek, P., 2013. "One-step robust estimation of fixed-effects panel data models," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 536-548.
    19. Lorenzo Camponovo & O. Scaillet & Fabio Trojani, 2013. "Predictability Hidden by Anomalous Observations," Swiss Finance Institute Research Paper Series 13-05, Swiss Finance Institute.
    20. Croux, Christophe & Flandre, Cécile & Haesbroeck, Gentiane, 2002. "The breakdown behavior of the maximum likelihood estimator in the logistic regression model," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 377-386, December.
    21. Luke A. Prendergast & Robert G. Staudte, 2017. "When large n is not enough – Distribution-free interval estimators for ratios of quantiles," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(3), pages 277-293, September.
    22. Tino Werner, 2023. "Quantitative robustness of instance ranking problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 335-368, April.
    23. 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.
    24. Hella, Heikki, 2003. "On robust ESACF identification of mixed ARIMA models," Bank of Finland Scientific Monographs, Bank of Finland, volume 0, number sm2003_027, December.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jorssb:v:65:y:2003:i:1:p:81-94. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.