Admissibility and minimaxity of generalized Bayes estimators for spherically symmetric family
AbstractWe give a sufficient condition for admissibility of generalized Bayes estimators of the location vector of spherically symmetric distribution under squared error loss. Compared to the known results for the multivariate normal case, our sufficient condition is very tight and is close to being a necessary condition. In particular, we establish the admissibility of generalized Bayes estimators with respect to the harmonic prior and priors with slightly heavier tail than the harmonic prior. We use the theory of regularly varying functions to construct a sequence of smooth proper priors approaching an improper prior fast enough for establishing the admissibility. We also discuss conditions of minimaxity of the generalized Bayes estimator with respect to the harmonic prior.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 99 (2008)
Issue (Month): 1 (January)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Maruyama, Yuzo, 2003. "Admissible minimax estimators of a mean vector of scale mixtures of multivariate normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 274-283, February.
- Bock, M. E., 1985. "Minimax estimators that shift towards a hypersphere for location vectors of spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 17(2), pages 127-147, October.
- Maruyama, Yuzo, 1998. "A Unified and Broadened Class of Admissible Minimax Estimators of a Multivariate Normal Mean," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 196-205, February.
- Maruyama, Yuzo, 2004. "Stein's idea and minimax admissible estimation of a multivariate normal mean," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 320-334, February.
- Brandwein, Ann Cohen, 1979. "Minimax estimation of the mean of spherically symmetric distributions under general quadratic loss," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 579-588, December.
- Maruyama, Yuzo, 2009. "An admissibility proof using an adaptive sequence of smoother proper priors approaching the target improper prior," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1845-1853, September.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.