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ASYMPTOTIC RISK BEHAVIOR OF MEAN VECTOR

AND VARIANCE ESTIMATORS

AND THE PROBLEM OF POSITIVE NORMAL MEAN

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ANDREW L. RUKHIN

*Department of Mathematics and Statistics, The University of Maryland,*

Baltimore County Campus, Baltimore, MD 21228-5398, U.S.A.

and University of Münster
(Received August 20, 1990; revised February 20, 1991)

**Abstract.**
Asymptotic risk behavior of estimators of the unknown
variance
and of the unknown mean vector in a multivariate normal distribution is
considered
for a general loss. It is shown that in both problems this characteristic
is related
to the risk in an estimation problem of a positive normal mean under
quadratic loss
function. A curious property of the Brewster-Zidek variance estimator of
the normal
variance is also noticed.

*Key words and phrases*:
Bowl-shaped loss function, Brewster-Zidek
estimator of normal variance, James-Stein estimator of normal mean,
relative risk
reduction, positive normal mean, Stein estimator of normal variance.

**Source**
( TeX ,
DVI ,
PS )