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Minimaxity in Estimation of Restricted Parameters

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  • Tatsuya Kubokawa

    (Faculty of Economics, The University of Tokyo)

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    Abstract

    This paper is concerned with estimation of the restricted parameters in location and/or scale families from a decision-theoretic point of view. A simple method is provided to show the minimaxity of the best equivariant and unrestricted estimators. This is based on a modification of the known method of Girshick and Savage (1951) and can be applied to more complicated cases of restriction in the location-scale family. Classes of minimax estimators are also constructed by using the IERD method of Kubokawa (1994a, b): Especially, the paper succeeds in constructing such a class for estimating a restricted mean in a normal distribution with an unknown variance.

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    Bibliographic Info

    Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-270.

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    Length: 24 pages
    Date of creation: Mar 2004
    Date of revision:
    Handle: RePEc:tky:fseres:2004cf270

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    Cited by:
    1. Kubokawa, Tatsuya & Strawderman, William E., 2011. "A unified approach to non-minimaxity of sets of linear combinations of restricted location estimators," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1429-1444, November.
    2. Tatsuya Kubokawa & William E. Strawderman, 2011. "A Unified Approach to Non-minimaxity of Sets of Linear Combinations of Restricted Location Estimators," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-786, CIRJE, Faculty of Economics, University of Tokyo.
    3. Hisayuki Tsukuma & Tatsuya Kubokawa, 2012. "Minimaxity in Estimation of Restricted and Non-restricted Scale Parameter Matrices," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-858, CIRJE, Faculty of Economics, University of Tokyo.
    4. Kubokawa, Tatsuya & Marchand, Éric & Strawderman, William E. & Turcotte, Jean-Philippe, 2013. "Minimaxity in predictive density estimation with parametric constraints," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 382-397.
    5. Tatsuya Kubokawa & William E. Strawderman, 2010. "Non-minimaxity of Linear Combinations of Restricted Location Estimators and Related Problems," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-749, CIRJE, Faculty of Economics, University of Tokyo.
    6. Tatsuya Kubokawa & �ric Marchand & William E. Strawderman & Jean-Philippe Turcotte, 2012. "Minimaxity in Predictive Density Estimation with Parametric Constraints," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-843, CIRJE, Faculty of Economics, University of Tokyo.
    7. Tatsuya Kubokawa, 2010. "Minimax Estimation of Linear Combinations of Restricted Location Parameters," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-723, CIRJE, Faculty of Economics, University of Tokyo.
    8. Mohammad Jafari Jozani & Éric Marchand & William Strawderman, 2014. "Estimation of a non-negative location parameter with unknown scale," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 66(4), pages 811-832, August.

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