IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i6p1313-1329.html
   My bibliography  Save this article

PLS regression: A directional signal-to-noise ratio approach

Author

Listed:
  • Druilhet, Pierre
  • Mom, Alain

Abstract

We present a new approach to univariate partial least squares regression (PLSR) based on directional signal-to-noise ratios (SNRs). We show how PLSR, unlike principal components regression, takes into account the actual value and not only the variance of the ordinary least squares (OLS) estimator. We find an orthogonal sequence of directions associated with decreasing SNR. Then, we state partial least squares estimators as least squares estimators constrained to be null on the last directions. We also give another procedure that shows how PLSR rebuilds the OLS estimator iteratively by seeking at each step the direction with the largest difference of signals over the noise. The latter approach does not involve any arbitrary scale or orthogonality constraints.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:6:p:1313-1329
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(05)00099-0
    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. 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.
    2. O. C. Lingjaerde & Nils Christophersen, 2000. "Shrinkage Structure of Partial Least Squares," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 459-473, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. 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.
    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. Druilhet, Pierre & Mom, Alain, 2008. "Shrinkage structure in biased regression," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 232-244, February.

    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. 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.
    2. Nicole Krämer, 2007. "An overview on the shrinkage properties of partial least squares regression," Computational Statistics, Springer, vol. 22(2), pages 249-273, July.
    3. 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.
    4. 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.
    5. 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.
    6. Ng, Serena, 2013. "Variable Selection in Predictive Regressions," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 752-789, Elsevier.
    7. 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.
    8. 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.
    9. Druilhet, Pierre & Mom, Alain, 2008. "Shrinkage structure in biased regression," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 232-244, February.
    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:97:y:2006:i:6:p:1313-1329. 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.