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Influence of observations on the misclassification probability in quadratic discriminant analysis

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  • Croux, Christophe
  • Joossens, Kristel

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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  • 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.
    • Handle: RePEc:eee:jmvana:v:96:y:2005:i:2:p:384-403
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    References listed on IDEAS

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    1. Norm A. Campbell, 1978. "The Influence Function as an Aid in Outlier Detection in Discriminant Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(3), pages 251-258, November.
    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. 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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    6. 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.
    7. Pires, Ana M. & Branco, João A., 2002. "Partial Influence Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 451-468, November.
    8. Hubert, Mia & Van Driessen, Katrien, 2004. "Fast and robust discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 301-320, March.
    9. 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.
    10. 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:

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    3. 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.
    4. Bianco, Ana & Boente, Graciela & Pires, Ana M. & Rodrigues, Isabel M., 2008. "Robust discrimination under a hierarchy on the scatter matrices," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1332-1357, July.
    5. Avner Bar-Hen & Servane Gey & Jean-Michel Poggi, 2015. "Influence Measures for CART Classification Trees," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 21-45, April.
    6. Bali, Juan Lucas & Boente, Graciela, 2017. "Robust estimators under a functional common principal components model," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 424-440.
    7. 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.

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