IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v99y2008i2p232-244.html
   My bibliography  Save this article

Shrinkage structure in biased regression

Author

Listed:
  • Druilhet, Pierre
  • Mom, Alain

Abstract

Biased regression is an alternative to ordinary least squares (OLS) regression, especially when explanatory variables are highly correlated. In this paper, we examine the geometrical structure of the shrinkage factors of biased estimators. We show that, in most cases, shrinkage factors cannot belong to [0,1] in all directions. We also compare the shrinkage factors of ridge regression (RR), principal component regression (PCR) and partial least-squares regression (PLSR) in the orthogonal directions obtained by the signal-to-noise ratio (SNR) algorithm. In these directions, we find that PLSR and RR behave well, whereas shrinkage factors of PCR have an erratic behaviour.

Suggested Citation

  • Druilhet, Pierre & Mom, Alain, 2008. "Shrinkage structure in biased regression," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 232-244, February.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:2:p:232-244
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(06)00102-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. 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.
    2. 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.
    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. 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.
    2. Zhun Cheng & Zhixiong Lu, 2021. "Research on Load Disturbance Based Variable Speed PID Control and a Novel Denoising Method Based Effect Evaluation of HST for Agricultural Machinery," Agriculture, MDPI, vol. 11(10), pages 1-18, October.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Nicole Krämer, 2007. "An overview on the shrinkage properties of partial least squares regression," Computational Statistics, Springer, vol. 22(2), pages 249-273, July.
    10. 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.

    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:99:y:2008:i:2:p:232-244. 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.