통합자연과학논문집 (Journal of Integrative Natural Science)

조선대학교 기초과학연구원 (The Basic Science Institute Chosun University)
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James-Stein Type Estimators Shrinking towards Projection Vector When the Norm is Restricted to an Interval

  • Baek, Hoh Yoo (Division of Mathematics and Informational Statistics, Wonkwang University) ;
  • Park, Su Hyang (Department of Informational Statistics, Graduate School, Wonkwang University)
  • 투고 : 2017.02.06
  • 심사 : 2017.03.25
  • 발행 : 2017.03.30
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초록

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.

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참고문헌

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