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The peculiar shrinkage properties of partial least squares regression

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  • Neil A. Butler
  • Michael C. Denham

Abstract

Partial least squares regression has been widely adopted within some areas as a useful alternative to ordinary least squares regression in the manner of other shrinkage methods such as principal components regression and ridge regression. In this paper we examine the nature of this shrinkage and demonstrate that partial least squares regression exhibits some undesirable properties.

Suggested Citation

  • Neil A. Butler & Michael C. Denham, 2000. "The peculiar shrinkage properties of partial least squares regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 585-593.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:3:p:585-593
    DOI: 10.1111/1467-9868.00252
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    Cited by:

    1. Hawkins, Douglas M. & Yin, Xiangrong, 2002. "A faster algorithm for ridge regression of reduced rank data," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 253-262, August.
    2. Kondylis, Athanassios & Whittaker, Joe, 2008. "Spectral preconditioning of Krylov spaces: Combining PLS and PC regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2588-2603, January.
    3. Hyonho Chun & Sündüz Keleş, 2010. "Sparse partial least squares regression for simultaneous dimension reduction and variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 3-25, January.
    4. Druilhet, Pierre & Mom, Alain, 2008. "Shrinkage structure in biased regression," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 232-244, February.
    5. Jie Huang & David Harrington, 2005. "Iterative Partial Least Squares with Right-Censored Data Analysis: A Comparison to Other Dimension Reduction Techniques," Biometrics, The International Biometric Society, vol. 61(1), pages 17-24, March.
    6. Subhash C. Basak & Denise Mills & Douglas M. Hawkins & Hisham A. El‐Masri, 2003. "Prediction of Human Blood: Air Partition Coefficient: A Comparison of Structure‐Based and Property‐Based Methods," Risk Analysis, John Wiley & Sons, vol. 23(6), pages 1173-1184, December.
    7. Nicole Krämer, 2007. "An overview on the shrinkage properties of partial least squares regression," Computational Statistics, Springer, vol. 22(2), pages 249-273, July.
    8. van Wieringen, Wessel N. & Kun, David & Hampel, Regina & Boulesteix, Anne-Laure, 2009. "Survival prediction using gene expression data: A review and comparison," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1590-1603, March.
    9. Anders Björkström, 2010. "Krylov Sequences as a Tool for Analysing Iterated Regression Algorithms," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 166-175, March.
    10. Druilhet, Pierre & Mom, Alain, 2006. "PLS regression: A directional signal-to-noise ratio approach," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1313-1329, July.

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