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High Breakdown Estimation for Multiple Populations with Applications to Discriminant Analysis

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  • 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
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    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. 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.
    3. Bashir, Shaheena & Carter, E. M., 2005. "High breakdown mixture discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 102-111, March.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Pires, Ana M. & Branco, João A., 2002. "Partial Influence Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 451-468, November.
    9. 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.
    10. 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).
    11. Davies, P. Laurie & Gather, U., 2002. "Breakdown and groups," Technical Reports 2002,57, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. repec:jss:jstsof:32:i03 is not listed on IDEAS
    17. 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.
    18. Hubert, Mia & Van Driessen, Katrien, 2004. "Fast and robust discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 301-320, March.
    19. 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).
    20. 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.
    21. Todorov, Valentin & Filzmoser, Peter, 2010. "Robust statistic for the one-way MANOVA," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 37-48, January.
    22. 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.
    23. Huang, Yufen & Wang, Sheng-Wen, 2013. "Influence analysis on the direction of optimal response," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1287-1299.
    24. 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.

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