Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions

Dominique Fourdrinier and William E. Strawderman

Journal of Multivariate Analysis, 2008, vol. 99, issue 4, 735-750

Abstract: Let X~f([short parallel]x-[theta][short parallel]2) and let [delta][pi](X) be the generalized Bayes estimator of [theta] with respect to a spherically symmetric prior, [pi]([short parallel][theta][short parallel]2), for loss [short parallel][delta]-[theta][short parallel]2. We show that if [pi](t) is superharmonic, non-increasing, and has a non-decreasing Laplacian, then the generalized Bayes estimator is minimax and dominates the usual minimax estimator [delta]0(X)=X under certain conditions on . The class of priors includes priors of the form for and hence includes the fundamental harmonic prior . The class of sampling distributions includes certain variance mixtures of normals and other functions f(t) of the form e-[alpha]t[beta] and e-[alpha]t+[beta][phi](t) which are not mixtures of normals. The proofs do not rely on boundness or monotonicity of the function r(t) in the representation of the Bayes estimator as .

Keywords: Minimax; estimators; Bayes; estimators; Quadratic; loss; Spherically; symmetric; distributions; Location; parameter; Superharmonic; priors (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(07)00054-1
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:99:y:2008:i:4:p:735-750

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().