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Shrinkage structure in biased regression


  • Druilhet, Pierre
  • Mom, Alain


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

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    References listed on IDEAS

    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.
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