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Ridge regression and its degrees of freedom

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  • Theo Dijkstra

Abstract

For ridge regression the degrees of freedom are commonly calculated by the trace of the matrix that transforms the vector of observations on the dependent variable into the ridge regression estimate of its expected value. For a fixed ridge parameter this is unobjectionable. When the ridge parameter is optimized on the same data, by minimization of the generalized cross validation criterion or Mallows $$\hbox {C}_{L}$$ C L , additional degrees of freedom are used however. We give formulae that take this into account. This allows of a proper assessment of ridge regression in competitions for the best predictor. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • Theo Dijkstra, 2014. "Ridge regression and its degrees of freedom," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(6), pages 3185-3193, November.
    • Handle: RePEc:spr:qualqt:v:48:y:2014:i:6:p:3185-3193
    DOI: 10.1007/s11135-013-9949-7
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    References listed on IDEAS

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    1. Bradley Efron, 2004. "The Estimation of Prediction Error: Covariance Penalties and Cross-Validation," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 619-632, January.
    2. Paul Anand & Graham Hunter & Ian Carter & Keith Dowding & Francesco Guala & Martin Van Hees, 2009. "The Development of Capability Indicators," Journal of Human Development and Capabilities, Taylor & Francis Journals, vol. 10(1), pages 125-152.
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    Cited by:

    1. Massimiliano Giacalone & Demetrio Panarello & Raffaele Mattera, 2018. "Multicollinearity in regression: an efficiency comparison between Lp-norm and least squares estimators," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1831-1859, July.
    2. Minda Ma & Ran Yan & Weiguang Cai, 2017. "An extended STIRPAT model-based methodology for evaluating the driving forces affecting carbon emissions in existing public building sector: evidence from China in 2000–2015," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 89(2), pages 741-756, November.
    3. Stefania Corsaro & Valentina De Simone & Zelda Marino & Salvatore Scognamiglio, 2024. "Learning fused lasso parameters in portfolio selection via neural networks," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(5), pages 4281-4299, October.
    4. Ma, Minda & Cai, Wei & Cai, Weiguang, 2018. "Carbon abatement in China's commercial building sector: A bottom-up measurement model based on Kaya-LMDI methods," Energy, Elsevier, vol. 165(PA), pages 350-368.

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