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Shrinkage estimation in general linear models

Author

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  • An, Lihua
  • Nkurunziza, Sévérien
  • Fung, Karen Y.
  • Krewski, Daniel
  • Luginaah, Isaac

Abstract

We propose a James-Stein-type shrinkage estimator for the parameter vector in a general linear model when it is suspected that some of the parameters may be restricted to a subspace. The James-Stein estimator is shown to demonstrate asymptotically superior risk performance relative to the conventional least squares estimator under quadratic loss. An extensive simulation study based on a multiple linear regression model and a logistic regression model further demonstrates the improved performance of this James-Stein estimator in finite samples. The application of this new estimator is illustrated using Ontario newborn infants data spanning four fiscal years.

Suggested Citation

  • An, Lihua & Nkurunziza, Sévérien & Fung, Karen Y. & Krewski, Daniel & Luginaah, Isaac, 2009. "Shrinkage estimation in general linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2537-2549, May.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:7:p:2537-2549
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    References listed on IDEAS

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    1. Dan J. Spitzner, 2005. "Risk‐reducing shrinkage estimation for generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 183-196, February.
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    3. Kim T-H. & White H., 2001. "James-Stein-Type Estimators in Large Samples With Application to the Least Absolute Deviations Estimator," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 697-705, June.
    4. Florens,Jean-Pierre & Marimoutou,Velayoudom & Peguin-Feissolle,Anne, 2007. "Econometric Modeling and Inference," Cambridge Books, Cambridge University Press, number 9780521700061, September.
    5. Khan, B.U. & Ahmed, S.E., 2006. "Comparisons of improved risk estimators of the multivariate mean vector," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 402-421, January.
    6. Florens,Jean-Pierre & Marimoutou,Velayoudom & Peguin-Feissolle,Anne, 2007. "Econometric Modeling and Inference," Cambridge Books, Cambridge University Press, number 9780521876407, April.
    7. Zou, Guohua & Wan, Alan T.K. & Wu, Xiaoyong & Chen, Ti, 2007. "Estimation of regression coefficients of interest when other regression coefficients are of no interest: The case of non-normal errors," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 803-810, April.
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    4. Brentnall, Adam R. & Crowder, Martin J. & Hand, David J., 2011. "Approximate repeated-measures shrinkage," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1150-1159, February.
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    7. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.

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