###
A CLASS OF MULTIPLE SHRINKAGE ESTIMATORS

###
C. S. WITHERS

*Applied Mathematics Division, Department of Scientific and Industrial Research,*

P. O. Box 1335, Wellington, New Zealand
(Received May 9, 1988; revised December 11, 1989)

**Abstract.**
Based on a sample of size *n*, we
investigate a class of estimators of the mean *theta* of a
*p*-variate normal distribution with independent components having unknown
covariance. This class includes the James-Stein estimator and Lindley's
estimator as special cases and was proposed by Stein. The mean squares
error improves on that of the sample mean for *p* __>__ 3. Simple
approximations for this improvement are given for large *n* or
*p*. Lindley's estimator improves on that of James and Stein if
either *n* is large, and the ``coefficient of variation'' of
*theta* is less than a certain increasing function of *p*, or if
*p* is large. An adaptive estimator is given which for large
samples always performs at least as well as these two estimators.

*Key words and phrases*:
Shrinkage estimates, multivariate
normal, loss.

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