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

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  • 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
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    References listed on IDEAS

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    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, 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.
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    Cited by:

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

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