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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
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    References listed on IDEAS

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

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