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Robust shrinkage estimators of the location parameter for elliptically symmetric distributions

Author

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  • Cellier, Dominique
  • Fourdrinier, Dominique
  • Robert, Christian

Abstract

The estimation of the location parameter of a spherically symmetric distribution was greatly improved by Berger and Brandwein. But the authors conditions on the shrinkage estimators depend upon the complete knowledge, up to the location parameter, of the distribution of the observations. We give sufficient conditions for uniform domination of the least squares estimator relatively to a class of elliptically symmetric distributions and a family of quadratic loss functions: our results can be applied to the particular case of estimation of a normal mean vector.

Suggested Citation

  • Cellier, Dominique & Fourdrinier, Dominique & Robert, Christian, 1989. "Robust shrinkage estimators of the location parameter for elliptically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 39-52, April.
    • Handle: RePEc:eee:jmvana:v:29:y:1989:i:1:p:39-52
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    Citations

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    Cited by:

    1. Dominique Fourdrinier & William Strawderman, 2015. "Robust minimax Stein estimation under invariant data-based loss for spherically and elliptically symmetric distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(4), pages 461-484, May.
    2. 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.
    3. Fourdrinier, Dominique & Strawderman, William, 2014. "On the non existence of unbiased estimators of risk for spherically symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 6-13.
    4. 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.
    5. M. Tan & L. Gleser, 1992. "Minimax estimators for location vectors in elliptical distributions with unknown scale parameter and its application to variance reduction in simulation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(3), pages 537-550, September.
    6. 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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