IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20000040.html
   My bibliography  Save this paper

Comprehensive Definitions of Breakdown-Points for Independent and Dependent Observations

Author

Listed:
  • Marc G. Genton

    (Massachusetts Institute of Technology)

  • André Lucas

    () (Vrije Universiteit Amsterdam)

Abstract

We provide a new definition of breakdown in finite samples with an extension to asymptotic breakdown. Previous definitions center around defining a critical region for either the parameter or the objective function. If for a particular outlier constellation the critical region is entered, breakdown is said to occur. In contract to the traditional approach, we leave the definition of the critical region implicit. Our definition encompasses all previousdefinitions of breakdown in both linear and non-linear regression settings. Insome cases, it leads to a different notion of breakdown than other procedures available. An advantage is that our new definition also applied to models for dependent observations (time-series, spatial statistics) where currenty breakdown definitions typically fail. We illustrate our points using examples from linear and non-linear regression as well as time-series and spatial statistics.

Suggested Citation

  • Marc G. Genton & André Lucas, 2000. "Comprehensive Definitions of Breakdown-Points for Independent and Dependent Observations," Tinbergen Institute Discussion Papers 00-040/2, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20000040
    as

    Download full text from publisher

    File URL: http://papers.tinbergen.nl/00040.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. He, Xuming, 1991. "A local breakdown property of robust tests in linear regression," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 294-305, August.
    2. Shinichi Sakata & Halbert White, 1998. "High Breakdown Point Conditional Dispersion Estimation with Application to S&P 500 Daily Returns Volatility," Econometrica, Econometric Society, vol. 66(3), pages 529-568, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Cizek, P., 2007. "General Trimmed Estimation : Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaces DP 2007-1)," Discussion Paper 2007-65, Tilburg University, Center for Economic Research.
    2. Alessio Farcomeni & Luca Greco, 2015. "S-estimation of hidden Markov models," Computational Statistics, Springer, vol. 30(1), pages 57-80, March.
    3. Cizek, P., 2005. "Trimmed Likelihood-based Estimation in Binary Regression Models," Discussion Paper 2005-108, Tilburg University, Center for Economic Research.
    4. 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 Technology, Institute of Organization and Management, vol. 1, pages 55-79.
    5. Lorenzo Camponovo & Olivier Scaillet & Fabio Trojani, 2016. "Predictability Hidden by Anomalous Observations," Papers 1612.05072, arXiv.org.
    6. 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.
    7. Luke A. Prendergast & Robert G. Staudte, 0. "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. 0, pages 1-17.
    8. Cizek, P. & Aquaro, M., 2015. "Robust Estimation and Moment Selection in Dynamic Fixed-effects Panel Data Models," Discussion Paper 2015-002, 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. 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.
    11. Cízek, Pavel, 2011. "Semiparametrically weighted robust estimation of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 774-788, January.
    12. Čížek, Pavel, 2012. "Semiparametric robust estimation of truncated and censored regression models," Journal of Econometrics, Elsevier, vol. 168(2), pages 347-366.
    13. Pavel Cizek & Wolfgang Härdle, 2006. "Robust Econometrics," SFB 649 Discussion Papers SFB649DP2006-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Genton, Mark G. & Ruiz-Gazen, Anne, 2009. "Visualizing Influential Observations in Dependent Data," TSE Working Papers 09-051, Toulouse School of Economics (TSE).
    15. Cizek, P., 2007. "Efficient Robust Estimation of Time-Series Regression Models," Discussion Paper 2007-95, Tilburg University, Center for Economic Research.
    16. repec:kap:jecinq:v:15:y:2017:i:3:d:10.1007_s10888-017-9347-9 is not listed on IDEAS
    17. Cizek, P., 2009. "Generalized Methods of Trimmed Moments," Discussion Paper 2009-25, Tilburg University, Center for Economic Research.

    More about this item

    Keywords

    Bias curve; Linear regression; Non-linear regression; Outliers; Spatial statistics; Statistical robustness; Time series;

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tin:wpaper:20000040. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tinbergen Office +31 (0)10-4088900). General contact details of provider: http://edirc.repec.org/data/tinbenl.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.