IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v190y2022ics0047259x22000306.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X22000306
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmva.2022.104993?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ulrike Genschel, 2018. "The Effect of Data Contamination in Sliced Inverse Regression and Finite Sample Breakdown Point," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 28-58, February.
    2. Coudret, R. & Girard, S. & Saracco, J., 2014. "A new sliced inverse regression method for multivariate response," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 285-299.
    3. 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.
    4. Luke A. Prendergast & Simon J. Sheather, 2013. "On Sensitivity of Inverse Response Plot Estimation and the Benefits of a Robust Estimation Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 219-237, June.
    5. Chiancone, Alessandro & Forbes, Florence & Girard, Stéphane, 2017. "Student Sliced Inverse Regression," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 441-456.
    6. Girard, Stéphane & Lorenzo, Hadrien & Saracco, Jérôme, 2022. "Advanced topics in Sliced Inverse Regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    7. Prendergast, Luke A., 2008. "Trimming influential observations for improved single-index model estimated sufficient summary plots," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5319-5327, August.
    8. Ayanendranath Basu & Abhijit Mandal & Nirian Martín & Leandro Pardo, 2019. "A Robust Wald-Type Test for Testing the Equality of Two Means from Log-Normal Samples," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 85-107, March.
    9. Heng-Hui Lue, 2015. "An Inverse-regression Method of Dependent Variable Transformation for Dimension Reduction with Non-linear Confounding," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 760-774, September.
    10. Stephen Babos & Andreas Artemiou, 2021. "Cumulative Median Estimation for Sufficient Dimension Reduction," Stats, MDPI, vol. 4(1), pages 1-8, February.
    11. Marie Chavent & Stéphane Girard & Vanessa Kuentz-Simonet & Benoit Liquet & Thi Nguyen & Jérôme Saracco, 2014. "A sliced inverse regression approach for data stream," Computational Statistics, Springer, vol. 29(5), pages 1129-1152, October.
    12. Boulesteix Anne-Laure, 2006. "Reader's Reaction to "Dimension Reduction for Classification with Gene Expression Microarray Data" by Dai et al (2006)," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-7, June.
    13. Zhou, Jianhui, 2009. "Robust dimension reduction based on canonical correlation," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 195-209, January.
    14. Graciela Boente & Frank Critchley & Liliana Orellana, 2007. "Influence functions of two families of robust estimators under proportional scatter matrices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 295-327, February.
    15. 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.
    16. Guochang Wang & Jianjun Zhou & Wuqing Wu & Min Chen, 2017. "Robust functional sliced inverse regression," Statistical Papers, Springer, vol. 58(1), pages 227-245, March.
    17. Jacques Bénasséni, 2018. "A correction of approximations used in sensitivity study of principal component analysis," Computational Statistics, Springer, vol. 33(4), pages 1939-1955, December.
    18. Flavia Esposito, 2021. "A Review on Initialization Methods for Nonnegative Matrix Factorization: Towards Omics Data Experiments," Mathematics, MDPI, vol. 9(9), pages 1-17, April.
    19. Lian, Heng & Li, Gaorong, 2014. "Series expansion for functional sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 150-165.
    20. A. García-Pérez, 2012. "A linear approximation to the power function of a test," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 855-875, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:190:y:2022:i:c:s0047259x22000306. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.