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The Influence Function as an Aid in Outlier Detection in Discriminant Analysis

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  • Norm A. Campbell

Abstract

The influence function is used to develop criteria for detecting outliers in discriminant analysis. For Mahalanobis' D2, the influence function is a quadratic function of the deviation of the discriminant score for the perturbed observation from the discriminant score for the mean of the corresponding group. A X2 approximation to the null distribution of the influence function values appears to be suitable for graphical representation.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssc:v:27:y:1978:i:3:p:251-258
    DOI: 10.2307/2347160
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    Citations

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    Cited by:

    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. W. Krzanowski, 1987. "A comparison between two distance-based discriminant principles," Journal of Classification, Springer;The Classification Society, vol. 4(1), pages 73-84, March.
    3. Kjell Johnson & William Rayens, 2007. "Influence function analysis applied to partial least squares," Computational Statistics, Springer, vol. 22(2), pages 293-306, July.
    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. Peter Verboon & Ivo Lans, 1994. "Robust canonical discriminant analysis," Psychometrika, Springer;The Psychometric Society, vol. 59(4), pages 485-507, December.
    6. Poon, Wai-Yin, 2006. "Identifying influential observations in logistic discriminant analysis," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1348-1355, July.
    7. Steel, S. J. & Louw, N., 2001. "Variable selection in discriminant analysis: measuring the influence of individual cases," Computational Statistics & Data Analysis, Elsevier, vol. 37(2), pages 249-260, August.
    8. 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.
    9. Pires, Ana M. & Branco, João A., 2002. "Partial Influence Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 451-468, November.
    10. 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.
    11. 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.
    12. 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.
    13. Tanaka, Yutaka & Zhang, Fanghong & Mori, Yuichi, 2003. "Local influence in principal component analysis: relationship between the local influence and influence function approaches revisited," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 143-160, October.

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