IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v72y2000i2p151-162.html
   My bibliography  Save this article

High Breakdown Estimation for Multiple Populations with Applications to Discriminant Analysis

Author

Listed:
  • He, Xuming
  • Fung, Wing K.

Abstract

We consider S-estimators of multivariate location and common dispersion matrix in multiple populations. Instead of averaging the robust estimates of the individual covariance matrices, as used by Todorov, Neykov and Neytchev (1990), the observations are pooled for estimating the common covariance more efficiently. Two such proposals are evaluated by a breakdown point analysis and Monte Carlo simulations. Their applications to the discriminant analysis are also considered.

Suggested Citation

  • He, Xuming & Fung, Wing K., 2000. "High Breakdown Estimation for Multiple Populations with Applications to Discriminant Analysis," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 151-162, February.
    • Handle: RePEc:eee:jmvana:v:72:y:2000:i:2:p:151-162
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(99)91857-2
    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.

    Citations

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


    Cited by:

    1. Valentin Todorov, 2007. "Robust selection of variables in linear discriminant analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 395-407, February.
    2. Matías Salibián-Barrera & Stefan Aelst & Gert Willems, 2008. "Fast and robust bootstrap," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 41-71, February.
    3. Croux, Christophe & Joossens, Kristel, 2005. "Influence of observations on the misclassification probability in quadratic discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 384-403, October.
    4. Van Aelst, Stefan & Willems, Gert, 2013. "Fast and Robust Bootstrap for Multivariate Inference: The R Package FRB," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 53(i03).
    5. Todorov, Valentin & Filzmoser, Peter, 2010. "Robust statistic for the one-way MANOVA," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 37-48, January.
    6. Davies, P. Laurie & Gather, U., 2002. "Breakdown and groups," Technical Reports 2002,57, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    7. Huang, Yufen & Kao, Tzu-Ling & Wang, Tai-Ho, 2007. "Influence functions and local influence in linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3844-3861, May.
    8. Stefan Van Aelst & Gert Willems, 2010. "Inference for robust canonical variate analysis," 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 181-197, September.
    9. Huang, Yufen & Cheng, Ching-Ren & Wang, Tai-Ho, 2008. "Pair-perturbation influence functions of nongaussianity by projection pursuit," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 3971-3987, April.
    10. Pires, Ana M. & Branco, João A., 2010. "Projection-pursuit approach to robust linear discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2464-2485, November.
    11. Claudio Agostinelli & Luca Greco, 2019. "Weighted likelihood estimation of multivariate location and scatter," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 756-784, September.
    12. Peter Filzmoser & Karel Hron & Matthias Templ, 2012. "Discriminant analysis for compositional data and robust parameter estimation," Computational Statistics, Springer, vol. 27(4), pages 585-604, December.
    13. Mia Hubert & Stephan Van der Veeken, 2010. "Robust classification for skewed data," 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(4), pages 239-254, December.
    14. Valentin Todorov, 2007. "Robust selection of variables in linear discriminant analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 395-407, February.
    15. Huang, Yufen & Wang, Sheng-Wen, 2013. "Influence analysis on the direction of optimal response," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1287-1299.
    16. Huang, Yufen & Cheng, Ching-Ren & Wang, Tai-Ho, 2007. "Influence analysis of non-Gaussianity by applying projection pursuit," Statistics & Probability Letters, Elsevier, vol. 77(14), pages 1515-1521, August.
    17. Md. Matiur Rahaman & Md. Nurul Haque Mollah, 2019. "Robustification of Gaussian Bayes Classifier by the Minimum β-Divergence Method," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 113-139, April.
    18. Sajobi, Tolulope T. & Lix, Lisa M. & Dansu, Bolanle M. & Laverty, William & Li, Longhai, 2012. "Robust descriptive discriminant analysis for repeated measures data," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2782-2794.
    19. repec:jss:jstsof:32:i03 is not listed on IDEAS
    20. Pires, Ana M. & Branco, João A., 2002. "Partial Influence Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 451-468, November.
    21. Zuo, Yijun, 2001. "Some quantitative relationships between two types of finite sample breakdown point," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 369-375, February.
    22. Hubert, Mia & Van Driessen, Katrien, 2004. "Fast and robust discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 301-320, March.
    23. Bashir, Shaheena & Carter, E. M., 2005. "High breakdown mixture discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 102-111, March.
    24. 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).

    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:72:y:2000:i:2:p:151-162. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.