IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v37y1998i4p331-340.html
   My bibliography  Save this article

Limit behavior of the empirical influence function of the median

Author

Listed:
  • Croux, Christophe

Abstract

The empirical influence function EIF(x, Tn; X) measures the influence of an observation x on the estimator Tn at a sample X of size n. In this note we show that the empirical influence function of the median is not a consistent estimator of the corresponding influence function. This observation leads to a reconsideration of the most -robustness property of the median. We will prove and show by simulations that the median is less robust to single outliers than commonly believed.

Suggested Citation

  • Croux, Christophe, 1998. "Limit behavior of the empirical influence function of the median," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 331-340, March.
  • Handle: RePEc:eee:stapro:v:37:y:1998:i:4:p:331-340
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(97)00135-1
    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. Oosterhoff, J., 1994. "Trimmed mean or sample median?," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 401-409, August.
    2. A. Christmann & U. Gather & G. Scholz, 1994. "Some properties of the length of the shortest half," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 48(3), pages 209-213, November.
    3. Cabrera, J. & Maguluri, G. & Singh, K., 1994. "An odd property of the sample median," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 349-354, March.
    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. Bar-Hen, Avner & Poggi, Jean-Michel, 2016. "Influence measures and stability for graphical models," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 145-154.
    2. Maria Iannario & Anna Clara Monti & Domenico Piccolo, 2016. "Robustness issues for cub models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 731-750, December.

    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. Mudholkar, Govind S. & Hutson, Alan D., 1997. "Asymmetric quasimedians: Remarks on an anomaly," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 261-268, March.
    2. Huang, J. S., 1999. "Third-order expansion of mean squared error of medians," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 185-192, April.
    3. Löw, Philipp & Osterburg, Bernhard, 2024. "Evaluation of nitrogen balances and nitrogen use efficiencies on farm level of the German agricultural sector," Agricultural Systems, Elsevier, vol. 213(C).
    4. Khachapon Nimdet & Nathorn Chaiyakunapruk & Kittaya Vichansavakul & Surachat Ngorsuraches, 2015. "A Systematic Review of Studies Eliciting Willingness-to-Pay per Quality-Adjusted Life Year: Does It Justify CE Threshold?," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-16, April.
    5. Hawkins, Douglas M. & Olive, David, 1999. "Applications and algorithms for least trimmed sum of absolute deviations regression," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 119-134, December.
    6. Christmann, Andreas, 1998. "On group sequential tests based on robust location and scale estimators in the two-sample problem," Technical Reports 1998,02, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    7. Luis J. Álvarez & María de los Llanos Matea, 1999. "Underlying Inflation Measures in Spain," Working Papers 9911, Banco de España.
    8. Luc Aucremanne, 2000. "The use of robust estimators as measures of core inflation," Working Paper Research 02, National Bank of Belgium.
    9. A. Christmann & U. Gather & G. Scholz, 1994. "Some properties of the length of the shortest half," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 48(3), pages 209-213, November.
    10. Duden, C. & Offermann, F., 2019. "Farmers' risk exposition and its drivers," 171st Seminar, September 5-6, 2019, Zürich, Switzerland 333722, European Association of Agricultural Economists.
    11. Guo, Jiin-Huarng & Luh, Wei-Ming, 2000. "An invertible transformation two-sample trimmed t-statistic under heterogeneity and nonnormality," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 1-7, August.

    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:37:y:1998:i:4:p:331-340. 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.