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Simultaneous estimation of normal precision matrices


  • Hisayuki Tsukuma

    (Department of Medical Informatics, Toho University)

  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)


This paper treats the problem of simultaneously estimating the precision matrices in multivariate normal distributions. A condition for improvement on the unbiased estimators of the precision matrices is derived under a quadratic loss function. The improvement condition is similar to the superharmonic condition established by Stein (1981). The condition allows us not only to provide various alternative estimators such as shrinkage type and enlargement type estimators for the unbiased estimators, but also to present a condition on a prior density under which the resulting generalized Bayes estimators dominate the unbiased estimators. Also, a unified method improving upon both the shrinkage and the enlargement type estimators is discussed.

Suggested Citation

  • Hisayuki Tsukuma & Tatsuya Kubokawa, 2006. "Simultaneous estimation of normal precision matrices," CIRJE F-Series CIRJE-F-459, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2006cf459

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    References listed on IDEAS

    1. Dey, Dipak K., 1987. "Improved estimation of a multinormal precision matrix," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 125-128, November.
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