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An extended class of minimax generalized Bayes estimators of regression coefficients

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  • Maruyama, Yuzo
  • Strawderman, William E.

Abstract

We derive minimax generalized Bayes estimators of regression coefficients in the general linear model with spherically symmetric errors under invariant quadratic loss for the case of unknown scale. The class of estimators generalizes the class considered in Maruyama and Strawderman [Y. Maruyama, W.E. Strawderman, A new class of generalized Bayes minimax ridge regression estimators, Ann. Statist., 33 (2005) 1753-1770] to include non-monotone shrinkage functions.

Suggested Citation

  • Maruyama, Yuzo & Strawderman, William E., 2009. "An extended class of minimax generalized Bayes estimators of regression coefficients," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2155-2166, November.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:10:p:2155-2166
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    References listed on IDEAS

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    1. Maruyama Yuzo, 2003. "A robust generalized Bayes estimator improving on the James-Stein estimator for spherically symmetric distributions," Statistics & Risk Modeling, De Gruyter, vol. 21(1/2003), pages 69-78, January.
    2. Maruyama, Yuzo, 1998. "A Unified and Broadened Class of Admissible Minimax Estimators of a Multivariate Normal Mean," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 196-205, February.
    3. Kubokawa, T. & Srivastava, M. S., 2001. "Robust Improvement in Estimation of a Mean Matrix in an Elliptically Contoured Distribution," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 138-152, January.
    4. Wells, Martin T. & Zhou, Gongfu, 2008. "Generalized Bayes minimax estimators of the mean of multivariate normal distribution with unknown variance," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2208-2220, November.
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    1. Aurélie Boisbunon & Stéphane Canu & Dominique Fourdrinier & William Strawderman & Martin T. Wells, 2014. "Akaike's Information Criterion, C p and Estimators of Loss for Elliptically Symmetric Distributions," International Statistical Review, International Statistical Institute, vol. 82(3), pages 422-439, December.

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