IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v71y1999i2p161-190.html
   My bibliography  Save this article

Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator

Author

Listed:
  • Croux, Christophe
  • Haesbroeck, Gentiane

Abstract

The minimum covariance determinant (MCD) scatter estimator is a highly robust estimator for the dispersion matrix of a multivariate, elliptically symmetric distribution. It is relatively fast to compute and intuitively appealing. In this note we derive its influence function and compute the asymptotic variances of its elements. A comparison with the one step reweighted MCD and with S-estimators is made. Also finite-sample results are reported.

Suggested Citation

  • Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
    • Handle: RePEc:eee:jmvana:v:71:y:1999:i:2:p:161-190
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(99)91839-0
    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. Hawkins, Douglas M., 1994. "The feasible solution algorithm for the minimum covariance determinant estimator in multivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 197-210, February.
    2. Rousseeuw, Peter J. & Croux, Christophe, 1994. "The bias of k-step M-estimators," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 411-420, August.
    3. Davies, Laurie, 1992. "An efficient Fréchet differentiable high breakdown multivariate location and dispersion estimator," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 311-327, February.
    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. Croux, Christophe & Haesbroeck, Gentiane, 1997. "An easy way to increase the finite-sample efficiency of the resampled minimum volume ellipsoid estimator," Computational Statistics & Data Analysis, Elsevier, vol. 25(2), pages 125-141, July.
    2. C. Croux & C. Dehon & A. Yadine, 2010. "The k-step spatial sign covariance matrix," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(2), pages 137-150, September.
    3. Hawkins, Douglas M. & Olive, David J., 1999. "Improved feasible solution algorithms for high breakdown estimation," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 1-11, March.
    4. Todorov, Valentin & Filzmoser, Peter, 2009. "An Object-Oriented Framework for Robust Multivariate Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i03).
    5. Hawkins, Douglas M., 1995. "Convergence of the feasible solution algorithm for least median of squares regression," Computational Statistics & Data Analysis, Elsevier, vol. 19(5), pages 519-538, May.
    6. Smirnov, Pavel O. & Shevlyakov, Georgy L., 2014. "Fast highly efficient and robust one-step M-estimators of scale based on Qn," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 153-158.
    7. Schyns, M. & Haesbroeck, G. & Critchley, F., 2010. "RelaxMCD: Smooth optimisation for the Minimum Covariance Determinant estimator," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 843-857, April.
    8. Schlittgen, Rainer & Schwabe, Rainer, 2001. "An alternative definition of the influence function," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 143-153, January.
    9. Woodruff, David L. & Reiners, Torsten, 2004. "Experiments with, and on, algorithms for maximum likelihood clustering," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 237-253, September.
    10. J. L. Alfaro & J. Fco. Ortega, 2009. "A comparison of robust alternatives to Hotelling's T2 control chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(12), pages 1385-1396.
    11. Berrendero, José R. & Zamar, Ruben H., 1999. "Global robustness of location and dispersion estimates," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 63-72, August.
    12. C. Croux & C. Dehon & A. Yadine, 2010. "The k-step spatial sign covariance matrix," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(2), pages 137-150, September.
    13. Cem Haydaroğlu & Bilal Gümüş, 2022. "Fault Detection in Distribution Network with the Cauchy-M Estimate—RVFLN Method," Energies, MDPI, vol. 16(1), pages 1-18, December.
    14. Gather, Ursula & Davies, P. Laurie, 2004. "Robust Statistics," Papers 2004,20, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    15. Sukru Acitas & Pelin Kasap & Birdal Senoglu & Olcay Arslan, 2013. "One-step M -estimators: Jones and Faddy's skewed t -distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(7), pages 1545-1560, July.
    16. Cheng, Tsung-Chi & Biswas, Atanu, 2008. "Maximum trimmed likelihood estimator for multivariate mixed continuous and categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2042-2065, January.
    17. Bianco, Ana & Boente, Graciela, 2002. "On the asymptotic behavior of one-step estimates in heteroscedastic regression models," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 33-47, November.
    18. Guoqing Wu & Chao Chen & Xuefeng Yan, 2011. "Modified minimum covariance determinant estimator and its application to outlier detection of chemical process data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 1007-1020, January.
    19. repec:jss:jstsof:32:i03 is not listed on IDEAS

    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:jmvana:v:71:y:1999:i:2:p:161-190. 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.