Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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An approach to improving the James-Stein estimator shrinking towards projection vectors

  • Park, Tae Ryong (Department of Computer Engineering, Seokyeong University) ;
  • Baek, Hoh Yoo (Division of Mathematics and Informational Statistics, Wonkwang University)
  • Received : 2014.08.23
  • Accepted : 2014.10.17
  • Published : 2014.11.30
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Abstract

Consider a p-variate normal distribution ($p-q{\geq}3$, q = rank($P_V$) with a projection matrix $P_V$). Using a simple property of noncentral chi square distribution, the generalized Bayes estimators dominating the James-Stein estimator shrinking towards projection vectors under quadratic loss are given based on the methods of Brown, Brewster and Zidek for estimating a normal variance. This result can be extended the cases where covariance matrix is completely unknown or ${\sum}={\sigma}^2I$ for an unknown scalar ${\sigma}^2$.

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References

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