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

Hisayuki Tsukuma and Tatsuya Kubokawa
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Hisayuki Tsukuma: Faculty of Medicine, Toho University
Tatsuya Kubokawa: Faculty of Economics, University of Tokyo

No CIRJE-F-858, CIRJE F-Series from CIRJE, 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.

Pages: 22 pages
Date: 2012-09
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2012cf858

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