IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2502.09145.html
   My bibliography  Save this paper

On (in)consistency of M-estimators under contamination

Author

Listed:
  • Jens Klooster
  • Bent Nielsen

Abstract

We consider robust location-scale estimators under contamination. We show that commonly used robust estimators such as the median and the Huber estimator are inconsistent under asymmetric contamination, while the Tukey estimator is consistent. In order to make nuisance parameter free inference based on the Tukey estimator a consistent scale estimator is required. However, standard robust scale estimators such as the interquartile range and the median absolute deviation are inconsistent under contamination.

Suggested Citation

  • Jens Klooster & Bent Nielsen, 2025. "On (in)consistency of M-estimators under contamination," Papers 2502.09145, arXiv.org.
    • Handle: RePEc:arx:papers:2502.09145
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2502.09145
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
    2. 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)

    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. Brent Kreider & Steven C. Hill, 2009. "Partially Identifying Treatment Effects with an Application to Covering the Uninsured," Journal of Human Resources, University of Wisconsin Press, vol. 44(2).
    2. Molinari, Francesca, 2010. "Missing Treatments," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 82-95.
    3. Christian Bontemps & Thierry Magnac & Eric Maurin, 2012. "Set Identified Linear Models," Econometrica, Econometric Society, vol. 80(3), pages 1129-1155, May.
    4. Bhalotra, Sonia & Clarke, Damian & Mühlrad, Hanna & Palme, Mårten, 2021. "Health and Labor Market Impacts of Twin Birth : Evidence from a Swedish IVF Policy Mandate," The Warwick Economics Research Paper Series (TWERPS) 1391, University of Warwick, Department of Economics.
    5. Koedel Cory & Leatherman Rebecca & Parsons Eric, 2012. "Test Measurement Error and Inference from Value-Added Models," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-37, November.
    6. Lothar Essig & Joachim K. Winter, 2009. "Item Non-Response to Financial Questions in Household Surveys: An Experimental Study of Interviewer and Mode Effects," Fiscal Studies, Institute for Fiscal Studies, vol. 30(Special I), pages 367-390, December.
    7. Karsten Marshall Elseth Rieck & Kjetil Telle, 2012. "Sick leave before, during and after pregnancy," Discussion Papers 690, Statistics Norway, Research Department.
    8. Esmerelda A. Ramalho & Richard Smith, 2003. "Discrete choice non-response," CeMMAP working papers 07/03, Institute for Fiscal Studies.
    9. Laffers, Lukas & Mellace, Giovanni, 2015. "A Note on Testing the LATE Assumptions," Discussion Papers on Economics 4/2015, University of Southern Denmark, Department of Economics.
    10. Guilhem Bascle, 2008. "Controlling for endogeneity with instrumental variables in strategic management research," Post-Print hal-00576795, HAL.
    11. Craig Gundersen & Brent Kreider, 2008. "Food Stamps and Food Insecurity: What Can Be Learned in the Presence of Nonclassical Measurement Error?," Journal of Human Resources, University of Wisconsin Press, vol. 43(2), pages 352-382.
    12. Kreider, Brent & Pepper, John V., 2007. "Disability and Employment: Reevaluating the Evidence in Light of Reporting Errors," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 432-441, June.
    13. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    14. Harry J. Paarsch & Jacques Robert, 2003. "Testing Equilibrium Behaviour At First-Price, Sealed-Bid Auctions With Discrete Bid Increments," CIRANO Working Papers 2003s-32, CIRANO.
    15. Ali Fakih & Paul Makdissi & Walid Marrouch & Rami V. Tabri & Myra Yazbeck, 2020. "Confidence in public institutions and the run up to the October 2019 uprising in Lebanon," Discussion Papers Series 629, School of Economics, University of Queensland, Australia.
    16. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
    17. Brent Kreider & John Pepper, 2008. "Inferring disability status from corrupt data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(3), pages 329-349.
    18. 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).
    19. Molinari, Francesca, 2020. "Microeconometrics with partial identification," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 355-486, Elsevier.
    20. Charles F. Manski, 2018. "Reasonable patient care under uncertainty," Health Economics, John Wiley & Sons, Ltd., vol. 27(10), pages 1397-1421, October.

    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:arx:papers:2502.09145. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.