통합자연과학논문집 (Journal of Integrative Natural Science)

조선대학교 기초과학연구원 (The Basic Science Institute Chosun University)
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Optimal Estimation within Class of James-Stein Type Decision Rules on the Known Norm

  • Baek, Hoh Yoo (Division of Mathematics and Informational Statistics, Wonkwang University)
  • 투고 : 2012.08.29
  • 심사 : 2012.09.25
  • 발행 : 2012.09.30
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초록

For the mean vector of a p-variate normal distribution ($p{\geq}3$), the optimal estimation within the class of James-Stein type decision rules under the quadratic loss are given when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}\underline{{\theta}}{\parallel}$ in known. It also demonstrated that the optimal estimation within the class of Lindley type decision rules under the same loss when the underlying distribution is the previous type and the norm ${\parallel}{\theta}-\overline{\theta}\underline{1}{\parallel}$ with $\overline{\theta}=\frac{1}{p}\sum\limits_{i=1}^{n}{\theta}_i$ and $\underline{1}=(1,{\cdots},1)^{\prime}$ is known.

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참고문헌

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