통합자연과학논문집 (Journal of Integrative Natural Science)

조선대학교 기초과학연구원 (The Basic Science Institute Chosun University)
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Estimators Shrinking towards Projection Vector for Multivariate Normal Mean Vector under the Norm with a Known Interval

  • Baek, Hoh Yoo (Division of Mathematics and Informational Statistics, Wonkwang University)
  • 투고 : 2018.09.11
  • 심사 : 2018.09.18
  • 발행 : 2018.09.30
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초록

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p-r{\geq}3)$, r = rank(K) with a projection matrix K under the quadratic loss, based on a sample $Y_1$, $Y_2$, ${\cdots}$, $Y_n$. In this paper a James-Stein type estimator with shrinkage form is given when it's variance distribution is specified and when the norm ${\parallel}{\theta}-K{\theta}{\parallel}$ is constrain, where K is an idempotent and symmetric matrix and rank(K) = r. It is characterized a minimal complete class of James-Stein type estimators in this case. And the subclass of James-Stein type estimators that dominate the sample mean is derived.

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연구 과제 주관 기관 : Wonkwang University

참고문헌

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