IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v33y1997i4p419-425.html
   My bibliography  Save this article

The breakdown value of the L1 estimator in contingency tables

Author

Listed:
  • Hubert, Mia

Abstract

First we derive the maximal breakdown value of regression equivariant estimators in two-way contingency tables under the loglinear independence model. We then prove that the L1 estimator achieves this maximal breakdown value. Finally, we illustrate how these results can be generalized towards the uniform association model for contingency tables with ordered categories.

Suggested Citation

  • Hubert, Mia, 1997. "The breakdown value of the L1 estimator in contingency tables," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 419-425, May.
    • Handle: RePEc:eee:stapro:v:33:y:1997:i:4:p:419-425
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(96)00156-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. He, Xuming, et al, 1990. "Tail Behavior of Regression Estimators and Their Breakdown Points," Econometrica, Econometric Society, vol. 58(5), pages 1195-1214, September.
    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. Eric Blankmeyer, 2018. "Measurement Errors as Bad Leverage Points," Papers 1807.02814, arXiv.org, revised Mar 2020.
    2. Davies, P. Laurie & Gather, U., 2002. "Breakdown and groups," Technical Reports 2002,57, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. 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.

    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. Cizek, P., 2009. "Generalized Methods of Trimmed Moments," Discussion Paper 2009-25, Tilburg University, Center for Economic Research.
    2. Vijverberg, Wim P. & Hasebe, Takuya, 2015. "GTL Regression: A Linear Model with Skewed and Thick-Tailed Disturbances," IZA Discussion Papers 8898, Institute of Labor Economics (IZA).
    3. Gather, Ursula & Einbeck, Jochen & Fried, Roland, 2005. "Weighted Repeated Median Smoothing and Filtering," Technical Reports 2005,33, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Jurecková, Jana, 2010. "Finite-sample distribution of regression quantiles," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1940-1946, December.
    5. Tamara Broderick & Ryan Giordano & Rachael Meager, 2020. "An Automatic Finite-Sample Robustness Metric: When Can Dropping a Little Data Make a Big Difference?," Papers 2011.14999, arXiv.org, revised Jul 2023.
    6. Jurecková, Jana, 2000. "Test of tails based on extreme regression quantiles," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 53-61, August.
    7. Christine Müller, 2011. "Data depth for simple orthogonal regression with application to crack orientation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 135-165, September.
    8. Mizera, Ivan & Müller, Christine H., 2002. "Breakdown points of Cauchy regression-scale estimators," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 79-89, March.
    9. Neykov, N.M. & Čížek, P. & Filzmoser, P. & Neytchev, P.N., 2012. "The least trimmed quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1757-1770.
    10. Čížek, Pavel, 2012. "Semiparametric robust estimation of truncated and censored regression models," Journal of Econometrics, Elsevier, vol. 168(2), pages 347-366.
    11. Janus, Thorsten, 2024. "Does export underreporting contribute to the resource curse?," World Development, Elsevier, vol. 181(C).
    12. Davies, P. Laurie & Fried, Roland & Gather, Ursula, 2002. "Robust signal extraction for on-line monitoring data," Technical Reports 2002,02, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    13. Barbe, Ph. & Broniatowski, M., 2004. "Blowing number of a distribution for a statistics and loyal estimators," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 465-475, October.
    14. Avi Giloni & Bhaskar Sengupta & Jeffrey S. Simonoff, 2006. "A mathematical programming approach for improving the robustness of least sum of absolute deviations regression," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 261-271, June.
    15. Giloni, Avi & Simonoff, Jeffrey S. & Sengupta, Bhaskar, 2006. "Robust weighted LAD regression," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3124-3140, July.
    16. Jurecková, Jana & Koenker, Roger & Portnoy, Stephen, 2001. "Tail behavior of the least-squares estimator," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 377-384, December.
    17. Hill, Jonathan B. & Aguilar, Mike, 2013. "Moment condition tests for heavy tailed time series," Journal of Econometrics, Elsevier, vol. 172(2), pages 255-274.
    18. Jana Jurecková, 2003. "Statistical tests on tail index of a probability distribution," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 151-190.
    19. Ke Zhu & Shiqing Ling, 2015. "LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 784-794, June.
    20. Salvador Flores, 2015. "Sharp non-asymptotic performance bounds for $$\ell _1$$ ℓ 1 and Huber robust regression estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 796-812, December.

    More about this item

    Keywords

    L1 regression Breakdown value Contingency tables Uniform association model;

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

    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:eee:stapro:v:33:y:1997:i:4:p:419-425. 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.