IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v32y2005i3p385-404.html
   My bibliography  Save this article

Influence Functions for Sliced Inverse Regression

Author

Listed:
  • L. A. PRENDERGAST

Abstract

. Sliced inverse regression (SIR) is a dimension reduction technique that is both efficient and simple to implement. The procedure itself relies heavily on estimates that are known to be highly non‐robust and, as such, the issue of robustness is often raised. This paper looks at the robustness of SIR by deriving and plotting the influence function for a variety of contamination structures. The sample influence function is also considered and used to highlight that common outlier detection and deletion methods may not be entirely useful to SIR. The asymptotic variance of the estimates is also derived for the single index model when the explanatory variable is known to be normally distributed. The asymptotic variance is then compared for varying choices of the number of slices for a simple model example.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:32:y:2005:i:3:p:385-404
    DOI: 10.1111/j.1467-9469.2005.00447.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9469.2005.00447.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9469.2005.00447.x?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Guochang Wang & Jianjun Zhou & Wuqing Wu & Min Chen, 2017. "Robust functional sliced inverse regression," Statistical Papers, Springer, vol. 58(1), pages 227-245, March.
    7. 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.
    8. Dong, Yuexiao & Yu, Zhou & Zhu, Liping, 2015. "Robust inverse regression for dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 71-81.

    More about this item

    Statistics

    Access and download statistics

    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:bla:scjsta:v:32:y:2005:i:3:p:385-404. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.