IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2014cf936.html
   My bibliography  Save this paper

On Improved Shrinkage Estimators for Concave Loss

Author

Listed:
  • Tatsuya Kubokawa

    (Faculty of Economics, The University of Tokyo)

  • Éric Marchand

    (Université de Sherbrooke, Departement de mathématiques)

  • William E. Strawderman

    (Rutgers University, Department of Statistics and Biostatistics,)

Abstract

We consider minimax shrinkage estimation of a location vector of a spherically symmetric distribution under a loss function which is a concave function of the usual squared error loss. In particular for distributions which are scale mixtures of normals (and somewhat more generally), and for concave loss functions whose derivatives are completely monotone (and somewhat more generally), we give classes of minimax shrinkage estimators where the shrinkage constants are larger than those currently in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:tky:fseres:2014cf936
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2014/2014cf936.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Strawderman, William E., 1974. "Minimax estimation of location parameters for certain spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 4(3), pages 255-264, September.
    3. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. Tatsuya Kubokawa & Éric Marchand & William E. Strawderman, 2014. "On Predictive Density Estimation for Location Families under Integrated L 2 and L 1 Losses," CIRJE F-Series CIRJE-F-935, CIRJE, Faculty of Economics, University of Tokyo.
    4. Kubokawa, Tatsuya & Marchand, Éric & Strawderman, William E., 2015. "On predictive density estimation for location families under integrated squared error loss," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 57-74.
    5. Marchand, Éric & Strawderman, William E., 2020. "On shrinkage estimation for balanced loss functions," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    6. Juan Pablo Atal & José Ignacio Cuesta & Felipe González & Cristóbal Otero, 2024. "The Economics of the Public Option: Evidence from Local Pharmaceutical Markets," American Economic Review, American Economic Association, vol. 114(3), pages 615-644, March.
    7. Péter Eso & Balázs Szentes, 2004. "The Price of Advice," Discussion Papers 1416, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Arve, Malin & Zwart, Gijsbert, 2023. "Optimal procurement and investment in new technologies under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 147(C).
    9. Alexandre de Corniere, 2013. "Search Advertising," Economics Series Working Papers 649, University of Oxford, Department of Economics.
    10. Andrew Rhodes & Jidong Zhou, 2019. "Consumer Search and Retail Market Structure," Management Science, INFORMS, vol. 67(6), pages 2607-2623, June.
    11. Dominique Fourdrinier & Othmane Kortbi & William Strawderman, 2014. "Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions with residual vector," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 285-296, February.
    12. Chakravarty, Surajeet & Kaplan, Todd R. & Myles, Gareth, 2018. "When costly voting is beneficial," Journal of Public Economics, Elsevier, vol. 167(C), pages 33-42.
    13. Schweizer, Nikolaus & Szech, Nora, 2015. "A quantitative version of Myerson regularity," Working Paper Series in Economics 76, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    14. Péter Eső & Balázs Szentes, 2007. "The price of advice," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 863-880, December.
    15. Rhodes, Andrew, 2011. "Multiproduct pricing and the Diamond Paradox," MPRA Paper 32511, University Library of Munich, Germany.
    16. Nocke, Volker & Peitz, Martin & Rosar, Frank, 2011. "Advance-purchase discounts as a price discrimination device," Journal of Economic Theory, Elsevier, vol. 146(1), pages 141-162, January.
    17. Mark J. McCabe & Christopher M. Snyder, 2015. "Does Online Availability Increase Citations? Theory and Evidence from a Panel of Economics and Business Journals," The Review of Economics and Statistics, MIT Press, vol. 97(1), pages 144-165, March.
    18. Allen Blackman, 2001. "Why don't Lenders Finance High-Return Technological Change in Developing-Country Agriculture?," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 83(4), pages 1024-1035.
    19. Albrecht, James & Anderson, Axel & Vroman, Susan, 2010. "Search by committee," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1386-1407, July.
    20. Madeleine Cule & Richard Samworth & Michael Stewart, 2010. "Maximum likelihood estimation of a multi‐dimensional log‐concave density," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 545-607, November.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:tky:fseres:2014cf936. 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: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.html .

    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.