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Influence of observations on the misclassification probability in quadratic discriminant analysis

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  • Croux, Christophe
  • Joossens, Kristel
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    Abstract

    In this paper it is studied how observations in the training sample affect the misclassification probability of a quadratic discriminant rule. An approach based on partial influence functions is followed. It allows to quantify the effect of observations in the training sample on the performance of the associated classification rule. Focus is on the effect of outliers on the misclassification rate, merely than on the estimates of the parameters of the quadratic discriminant rule. The expression for the partial influence function is then used to construct a diagnostic tool for detecting influential observations. Applications on real data sets are provided.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 96 (2005)
    Issue (Month): 2 (October)
    Pages: 384-403

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    Handle: RePEc:eee:jmvana:v:96:y:2005:i:2:p:384-403

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    Related research

    Keywords: Classification Diagnostics Misclassification probability Outliers Partial influence functions Quadratic discriminant analysis;

    References

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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.
    2. Fung, Wing K., 1995. "Detecting influential observations for estimated probabilities in multiple discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 20(5), pages 557-568, November.
    3. 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.
    4. Hubert, Mia & Van Driessen, Katrien, 2004. "Fast and robust discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 301-320, March.
    5. McFarland, H. Richard & Richards, Donald St. P., 2002. "Exact Misclassification Probabilities for Plug-In Normal Quadratic Discriminant Functions: II. The Heterogeneous Case," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 299-330, August.
    6. Pires, Ana M. & Branco, João A., 2002. "Partial Influence Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 451-468, November.
    7. Fung, Wing-Kam, 1992. "Some diagnostic measures in discriminant analysis," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 279-285, March.
    8. Graciela Boente, 2002. "Influence functions and outlier detection under the common principal components model: A robust approach," Biometrika, Biometrika Trust, vol. 89(4), pages 861-875, December.
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    Cited by:
    1. Salvador, B. & Fernandez, M.A. & Martin, I. & Rueda, C., 2008. "Robustness of classification rules that incorporate additional information," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2489-2495, January.
    2. 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.

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