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High breakdown mixture discriminant analysis

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  • Bashir, Shaheena
  • Carter, E. M.

Abstract

Robust S-estimation is proposed for multivariate Gaussian mixture models generalizing the work of Hastie and Tibshirani (J. Roy. Statist. Soc. Ser. B 58 (1996) 155). In the case of Gaussian Mixture models, the unknown location and scale parameters are estimated by the EM algorithm. In the presence of outliers, the maximum likelihood estimators of the unknown parameters are affected, resulting in the misclassification of the observations. The robust S-estimators of the unknown parameters replace the non-robust estimators from M-step of the EM algorithm. The results were compared with the standard mixture discriminant analysis approach using the probability of misclassification criterion. This comparison showed a slight reduction in the average probability of misclassification using robust S-estimators as compared to the standard maximum likelihood estimators.

Suggested Citation

  • Bashir, Shaheena & Carter, E. M., 2005. "High breakdown mixture discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 102-111, March.
    • Handle: RePEc:eee:jmvana:v:93:y:2005:i:1:p:102-111
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    References listed on IDEAS

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    1. 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.
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    1. Alessio Farcomeni & Luca Greco, 2015. "S-estimation of hidden Markov models," Computational Statistics, Springer, vol. 30(1), pages 57-80, March.
    2. Christophe Croux & Catherine Dehon & Abdelilah Yadine, 2011. "On the Optimality of Multivariate S‐Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(2), pages 332-341, June.
    3. Christophe Croux & Catherine Dehon & Abdelilah Yadine, 2011. "On the Optimality of Multivariate S‐Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(2), pages 332-341, June.
    4. Marmion, Mathieu & Luoto, Miska & Heikkinen, Risto K. & Thuiller, Wilfried, 2009. "The performance of state-of-the-art modelling techniques depends on geographical distribution of species," Ecological Modelling, Elsevier, vol. 220(24), pages 3512-3520.

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