IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v99y2008i1p50-73.html
   My bibliography  Save this article

Admissibility and minimaxity of generalized Bayes estimators for spherically symmetric family

Author

Listed:
  • Maruyama, Yazo
  • Takemura, Akimichi

Abstract

We 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.

Suggested Citation

  • Maruyama, Yazo & Takemura, Akimichi, 2008. "Admissibility and minimaxity of generalized Bayes estimators for spherically symmetric family," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 50-73, January.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:1:p:50-73
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(07)00005-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Xu, Jian-Lun & Izmirlian, Grant, 2006. "Estimation of location parameters for spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 514-525, February.
    3. 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.
    4. Fourdrinier, Dominique & Strawderman, William E., 2008. "A unified and generalized set of shrinkage bounds on minimax Stein estimates," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2221-2233, November.
    5. Chaturvedi Anoop & Mishra Sandeep, 2019. "Generalized Bayes Estimation Of Spatial Autoregressive Models," Statistics in Transition New Series, Polish Statistical Association, vol. 20(2), pages 15-32, June.
    6. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2017. "Proper Bayes and minimax predictive densities related to estimation of a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 138-150.
    7. Zinodiny, S. & Strawderman, W.E. & Parsian, A., 2011. "Bayes minimax estimation of the multivariate normal mean vector for the case of common unknown variance," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1256-1262, October.
    8. Kubokawa, Tatsuya & Marchand, Éric & Strawderman, William E., 2015. "On improved shrinkage estimators for concave loss," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 241-246.
    9. Maruyama, Yuzo & Strawderman, William E., 2009. "An extended class of minimax generalized Bayes estimators of regression coefficients," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2155-2166, November.
    10. Tatsuya Kubokawa & Éric Marchand & William E. Strawderman, 2014. "On Improved Shrinkage Estimators for Concave Loss," CIRJE F-Series CIRJE-F-936, CIRJE, Faculty of Economics, University of Tokyo.
    11. Fourdrinier, Dominique & Strawderman, William E., 2008. "Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 735-750, April.
    12. Shalabh & H. Toutenburg & C. Heumann, 2008. "Mean squared error matrix comparison of least aquares and Stein-rule estimators for regression coefficients under non-normal disturbances," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 285-298.
    13. Yuzo Maruyama & William Strawderman, 2005. "Necessary conditions for dominating the James-Stein estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 157-165, March.
    14. Kuriki, Satoshi & Takemura, Akimichi, 2000. "Shrinkage Estimation towards a Closed Convex Set with a Smooth Boundary," Journal of Multivariate Analysis, Elsevier, vol. 75(1), pages 79-111, October.
    15. Anoop Chaturvedi & Shalabh & Sandeep Mishra, 2021. "Generalized Bayes Estimator for Spatial Durbin Model," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 267-285, December.
    16. Ann Brandwein & Stefan Ralescu & William Strawderman, 1993. "Shrinkage estimators of the location parameter for certain spherically symmetric distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 551-565, September.
    17. 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.
    18. Peter Hall & You‐Jun Yang, 2010. "Ordering and selecting components in multivariate or functional data linear prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 93-110, January.
    19. Hiroyuki Kashima, 2005. "An application of a minimax Bayes rule and shrinkage estimators to the portofolio selection problem under the Bayesian approach," Statistical Papers, Springer, vol. 46(4), pages 523-540, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:99:y:2008:i:1:p:50-73. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.