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Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions with residual vector

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  • Dominique Fourdrinier
  • Othmane Kortbi
  • William Strawderman

Abstract

We consider estimation of the mean vector, $$\theta $$ , of a spherically symmetric distribution with known scale parameter under quadratic loss and when a residual vector is available. We show minimaxity of generalized Bayes estimators corresponding to superharmonic priors with a non decreasing Laplacian of the form $$\pi (\Vert \theta \Vert ^{2})$$ , under certain conditions on the generating function $$f(\cdot )$$ of the sampling distributions. The class of sampling distributions includes certain variance mixtures of normals. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Dominique Fourdrinier & Othmane Kortbi & William Strawderman, 2014. "Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions with residual vector," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 285-296, February.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:2:p:285-296
    DOI: 10.1007/s00184-013-0437-9
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    References listed on IDEAS

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    1. Fourdrinier, Dominique & Kortbi, Othmane & Strawderman, William E., 2008. "Bayes minimax estimators of the mean of a scale mixture of multivariate normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 74-93, January.
    2. Strawderman, William E., 1974. "Minimax estimation of location parameters for certain spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 4(3), pages 255-264, September.
    3. Fourdrinier, Dominique & Strawderman, William E. & Wells, Martin T., 2003. "Robust shrinkage estimation for elliptically symmetric distributions with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 24-39, April.
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