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Shrinkage Structure of Partial Least Squares

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  • O. C. Lingjaerde
  • Nils Christophersen

Abstract

Partial least squares regression (PLS) is one method to estimate parameters in a linear model when predictor variables are nearly collinear. One way to characterize PLS is in terms of the scaling (shrinkage or expansion) along each eigenvector of the predictor correlation matrix. This characterization is useful in providing a link between PLS and other shrinkage estimators, such as principal components regression (PCR) and ridge regression (RR), thus facilitating a direct comparison of PLS with these methods. This paper gives a detailed analysis of the shrinkage structure of PLS, and several new results are presented regarding the nature and extent of shrinkage.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:27:y:2000:i:3:p:459-473
    DOI: 10.1111/1467-9469.00201
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    Cited by:

    1. Nicole Krämer, 2007. "An overview on the shrinkage properties of partial least squares regression," Computational Statistics, Springer, vol. 22(2), pages 249-273, July.
    2. 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.
    3. 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.
    4. 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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