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Influence functions for linear discriminant analysis: Sensitivity analysis and efficient influence diagnostics

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  • Prendergast, Luke A.
  • Smith, Jodie A.

Abstract

Whilst influence functions for linear discriminant analysis (LDA) have been found for a single discriminant when dealing with two groups, until now these have not been derived in the setting of a general number of groups. In this paper we explore the relationship between Sliced Inverse Regression (SIR) and LDA, and exploit this relationship to develop influence functions for LDA from those already derived for SIR. These influence functions can be used to understand robustness properties of LDA and also to detect influential observations in practice. We illustrate the usefulness of these via their application to a real data set.

Suggested Citation

  • Prendergast, Luke A. & Smith, Jodie A., 2022. "Influence functions for linear discriminant analysis: Sensitivity analysis and efficient influence diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:jmvana:v:190:y:2022:i:c:s0047259x22000306
    DOI: 10.1016/j.jmva.2022.104993
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    References listed on IDEAS

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    1. Luke A. Prendergast & Jodie A. Smith, 2010. "Influence Functions for Dimension Reduction Methods: An Example Influence Study of Principal Hessian Direction Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 588-611, December.
    2. Luke A. Prendergast, 2007. "Implications of influence function analysis for sliced inverse regression and sliced average variance estimation," Biometrika, Biometrika Trust, vol. 94(3), pages 585-601.
    3. Dong, Yuexiao & Yu, Zhou & Zhu, Liping, 2015. "Robust inverse regression for dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 71-81.
    4. Benoît Liquet & Jérôme Saracco, 2012. "A graphical tool for selecting the number of slices and the dimension of the model in SIR and SAVE approaches," Computational Statistics, Springer, vol. 27(1), pages 103-125, March.
    5. L. A. Prendergast, 2005. "Influence Functions for Sliced Inverse Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 385-404, September.
    6. Prendergast, Luke A. & Li Wai Suen, Connie, 2011. "A new and practical influence measure for subsets of covariance matrix sample principal components with applications to high dimensional datasets," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 752-764, January.
    7. Pires, Ana M. & Branco, João A., 2002. "Partial Influence Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 451-468, November.
    8. Dai Jian J & Lieu Linh & Rocke David, 2006. "Dimension Reduction for Classification with Gene Expression Microarray Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-21, February.
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