The Stein Phenomenon in Simultaneous Estimation of Normal Precisions

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

No CIRJE-F-473, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: In this paper, the simultaneous estimation of the precision parameters of k normal distributions is considered under the squared loss function in a decision-theoretic framework. Several classes of minimax estimators are derived by using the chi-square identity, and the generalized Bayes minimax estimators are developed out of the classes. It is also shown that the improvement on the unbiased estimators is characterized by the superharmonic function. This corresponds to Stein (1981)'s result in simultaneous estimation of normal means.

Pages: 24 pages
Date: 2007-02
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2007cf473

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