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On improved shrinkage estimators for concave loss

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  • Kubokawa, Tatsuya
  • Marchand, Éric
  • Strawderman, William E.

Abstract

We consider minimax shrinkage estimation of location for spherically symmetric distributions under a concave function of the usual squared error loss. Scale mixtures of normal distributions and losses with completely monotone derivatives are featured.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:241-246
    DOI: 10.1016/j.spl.2014.09.024
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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    Cited by:

    1. Fourdrinier, Dominique & Marchand, Éric & Strawderman, William E., 2019. "On efficient prediction and predictive density estimation for normal and spherically symmetric models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 18-25.
    2. Marchand, Éric & Strawderman, William E., 2020. "On shrinkage estimation for balanced loss functions," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    3. Ghannam, Mai & Nkurunziza, Sévérien, 2023. "Tensor Stein-rules in a generalized tensor regression model," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    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.

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