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Influence Functions for Sliced Inverse Regression

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  • 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
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    Cited by:

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

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