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Minimaxity in Estimation of Restricted and Non-restricted Scale Parameter Matrices

Author

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  • Hisayuki Tsukuma

    (Faculty of Medicine, Toho University)

  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

Abstract

In estimation of the normal covariance matrix, nding a least favorable sequence of prior distributions has been an open question for a long time. In this paper, we address the classical problem and succeed in construction of such a sequence, which establishes minimaxity of the best equivariant estimator. We also derive uni ed conditions for a sequence of prior distributions to be least favorable in the general estimation problem with an invariance structure. These uni ed conditions are applied to both restricted and non-restricted cases of parameters, and we give a couple of examples which show minimaxity of the best equivariant estimators under restrictions of the covariance matrix.

Suggested Citation

  • Hisayuki Tsukuma & Tatsuya Kubokawa, 2012. "Minimaxity in Estimation of Restricted and Non-restricted Scale Parameter Matrices," CIRJE F-Series CIRJE-F-858, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2012cf858
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2012/2012cf858.pdf
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    References listed on IDEAS

    as
    1. Tatsuya Kubokawa, 2004. "Minimaxity in Estimation of Restricted Parameters," CIRJE F-Series CIRJE-F-270, CIRJE, Faculty of Economics, University of Tokyo.
    2. Tatsuya Kubokawa & Éric Marchand & William E. Strawderman & Jean-Philippe Turcotte, 2012. "Minimaxity in Predictive Density Estimation with Parametric Constraints," CIRJE F-Series CIRJE-F-843, CIRJE, Faculty of Economics, University of Tokyo.
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    1. Hisayuki Tsukuma & Tatsuya Kubokawa, 2015. "Minimaxity in estimation of restricted and non-restricted scale parameter matrices," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 261-285, April.

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