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

Dominique Fourdrinier; Othmane Kortbi; William E. Strawderman

doi:10.1007/s00184-013-0437-9

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

Dominique Fourdrinier, Othmane Kortbi, William E. Strawderman

Research output: Contribution to journal › Article › peer-review

Abstract

We consider estimation of the mean vector, θ, 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 π(||θ||2), under certain conditions on the generating function f (·) of the sampling distributions. The class of sampling distributions includes certain variance mixtures of normals.

Original language	English
Pages (from-to)	285-296
Number of pages	12
Journal	Metrika
Volume	77
Issue number	2
DOIs	https://doi.org/10.1007/s00184-013-0437-9
Publication status	Published - Apr 11 2013
Externally published	Yes

Keywords

Bayes estimators
Minimax estimators
Quadratic loss
Spherical symmetry

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s00184-013-0437-9

Cite this

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abstract = "We consider estimation of the mean vector, θ, 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 π(||θ||2), under certain conditions on the generating function f (·) of the sampling distributions. The class of sampling distributions includes certain variance mixtures of normals.",

keywords = "Bayes estimators, Minimax estimators, Quadratic loss, Spherical symmetry",

author = "Dominique Fourdrinier and Othmane Kortbi and Strawderman, {William E.}",

note = "Funding Information: 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 Universit{\'e} de Sherbrooke, Othmane Kortbi benefited from financial support from several sources and he wishes to thank, in particular, the Institut de sciences math{\'e}matiques (ISM) and the Centre de recherches math{\'e}matiques (CRM). This work was also partially supported by a grant from the Simons Foundation (209035 to William Strawderman). Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2013.",

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AU - Kortbi, Othmane

AU - Strawderman, William E.

N1 - Funding Information: 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). Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2013.

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N2 - We consider estimation of the mean vector, θ, 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 π(||θ||2), under certain conditions on the generating function f (·) of the sampling distributions. The class of sampling distributions includes certain variance mixtures of normals.

AB - We consider estimation of the mean vector, θ, 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 π(||θ||2), under certain conditions on the generating function f (·) of the sampling distributions. The class of sampling distributions includes certain variance mixtures of normals.

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KW - Minimax estimators

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KW - Spherical symmetry

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

Abstract

Keywords

ASJC Scopus subject areas

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