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Influence of observations on the misclassification probability in quadratic discriminant analysis

Listed author(s):
  • Croux, Christophe
  • Joossens, Kristel
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    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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    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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    1. 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.
    2. 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.
    3. Fung, Wing-Kam, 1992. "Some diagnostic measures in discriminant analysis," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 279-285, March.
    4. Pison, Greet & Rousseeuw, Peter J. & Filzmoser, Peter & Croux, Christophe, 2003. "Robust factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 145-172, January.
    5. 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.
    6. Pires, Ana M. & Branco, João A., 2002. "Partial Influence Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 451-468, November.
    7. Hubert, Mia & Van Driessen, Katrien, 2004. "Fast and robust discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 301-320, March.
    8. 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.
    9. 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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