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.
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Acknowledgments
The authors would like to thank an associate editor for his/her careful reading and for his/her useful comments on the paper. During his Ph.D. studies at the Université de Sherbrooke, Othmane Kortbi benefited from financial support from several sources and he wishes to thank, in particular, the Institut de sciences mathématiques (ISM) and the Centre de recherches mathématiques (CRM). This work was also partially supported by a grant from the Simons Foundation (\(\#\)209035 to William Strawderman).
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Fourdrinier, D., Kortbi, O. & Strawderman, W.E. Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions with residual vector. Metrika 77, 285–296 (2014). https://doi.org/10.1007/s00184-013-0437-9
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DOI: https://doi.org/10.1007/s00184-013-0437-9