• Title/Summary/Keyword: James-Stein Type Decision Rule

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James-Stein Type Estimators Shrinking towards Projection Vector When the Norm is Restricted to an Interval

  • Baek, Hoh Yoo;Park, Su Hyang
    • Journal of Integrative Natural Science
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    • v.10 no.1
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    • pp.33-39
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    • 2017
  • Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p-q{\geq}3)$, $q=rank(P_V)$ with a projection matrix $P_v$ under the quadratic loss, based on a sample $X_1$, $X_2$, ${\cdots}$, $X_n$. We find a James-Stein type decision rule which shrinks towards projection vector when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}{\theta}-P_V{\theta}{\parallel}$ is restricted to a known interval, where $P_V$ is an idempotent and projection matrix and rank $(P_V)=q$. In this case, we characterize a minimal complete class within the class of James-Stein type decision rules. We also characterize the subclass of James-Stein type decision rules that dominate the sample mean.

Improvement of the Modified James-Stein Estimator with Shrinkage Point and Constraints on the Norm

  • Kim, Jae Hyun;Baek, Hoh Yoo
    • Journal of Integrative Natural Science
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    • v.6 no.4
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    • pp.251-255
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    • 2013
  • For the mean vector of a p-variate normal distribution ($p{\geq}4$), the optimal estimation within the class of modified James-Stein type decision rules under the quadratic loss is given when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}{\theta}-\bar{\theta}1{\parallel}$ it known.

Optimal Estimation within Class of James-Stein Type Decision Rules on the Known Norm

  • Baek, Hoh Yoo
    • Journal of Integrative Natural Science
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    • v.5 no.3
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    • pp.186-189
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    • 2012
  • 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.