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Concentration reversals in ridge regression

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  • Jensen, D.R.
  • Ramirez, D.E.

Abstract

Ridge regression is often the method of choice for approaching ill-conditioned systems. A canonical form identifies regions in the parameter space where Ordinary Least Squares is problematic. A curious but unrecognized property of ridge solutions emerges: Under spherical errors with or without moments, the relative concentrations of the canonical estimators reverse as the ridge scalar evolves, the estimators least concentrated under being most concentrated under ridge regression, and conversely.

Suggested Citation

  • Jensen, D.R. & Ramirez, D.E., 2009. "Concentration reversals in ridge regression," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2237-2241, November.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:21:p:2237-2241
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    References listed on IDEAS

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    1. Rolf Sundberg, 1999. "Multivariate Calibration — Direct and Indirect Regression Methodology," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 161-207, June.
    2. Jensen, D. R., 1997. "Symmetry and Unimodality in Linear Inference," Journal of Multivariate Analysis, Elsevier, vol. 60(2), pages 188-202, February.
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