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ESTIMATION OF A COMMON MULTIVARIATE NORMAL

MEAN VECTOR

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K. KRISHNAMOORTHY

*Department of Statistics, Temple University, Philadelphia, PA 19122, U.S.A.*
(Received December 4, 1989; revised June 6, 1990)

**Abstract.**
Let *X*_{1},...., *X*_{N} be independent
observations from *N*_{p}(*mu*, *Sigma*_{1}) and *Y*_{1},....,
*Y*_{N} be independent observations from *N*_{p}(*mu*, *Sigma*_{2}).
Assume that *X*_{i}'s and *Y*_{i}'s are independent. An
unbiased estimator of *mu* which dominates the sample mean
\bar *X* for *p* __>__ 1 under the loss function *L*(*mu*,
^{^}*mu*) = (^{^}*mu* - *mu*)'*Sigma*_{1}^{-1}(^{^}*mu*-*mu*) is suggested. The
exact risk (under *L*) of the new estimator is also
evaluated.

*Key words and phrases*:
Common mean vector,
unbiased estimator, Wishart and noncentral Wishart
distributions.

**Source**
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