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Minimaxity in estimation of restricted and non-restricted scale parameter matrices

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  • Hisayuki Tsukuma
  • Tatsuya Kubokawa

Abstract

In estimation of the normal covariance matrix, finding a least favorable sequence of prior distributions has been an open question for a long time. This paper addresses the classical problem and accomplishes the specification of such a sequence, which establishes minimaxity of the best equivariant estimator. This result is extended to the estimation of scale parameter matrix in an elliptically contoured distribution model. The methodology based on a least favorable sequence of prior distributions is applied to both restricted and non-restricted cases of parameters, and we give some examples which show minimaxity of the best equivariant estimators under restrictions of scale parameter matrix. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:2:p:261-285
    DOI: 10.1007/s10463-014-0449-x
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    References listed on IDEAS

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    1. Éric Marchand & William Strawderman, 2005. "Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 129-143, March.
    2. 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.
    3. 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.
    4. Tatsuya Kubokawa, 2004. "Minimaxity in Estimation of Restricted Parameters," CIRJE F-Series CIRJE-F-270, CIRJE, Faculty of Economics, University of Tokyo.
    5. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2011. "Modifying estimators of ordered positive parameters under the Stein loss," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 164-181, January.
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