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The Stein Phenomenon in Simultaneous Estimation of Normal Precisions

Author

Listed:
  • Hisayuki Tsukuma

    (School of Medicine, Toho University)

  • Tatsuya Kubokawa

    (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.

Suggested Citation

  • Hisayuki Tsukuma & Tatsuya Kubokawa, 2007. "The Stein Phenomenon in Simultaneous Estimation of Normal Precisions," CIRJE F-Series CIRJE-F-473, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2007cf473
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