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APPROXIMATE BAYESIAN SHRINKAGE ESTIMATION

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WANG-SHU LU

*Department of Statistics, College of Arts and Science, University of Missouri-Columbia,*

222 Math Sciences Bldg., Columbia, MO 65211, U.S.A.
(Received March 8, 1993; revised February 8, 1994)

**Abstract.**
A Bayesian shrinkage estimate for the mean in the
generalized linear empirical Bayes model is proposed. The posterior mean
under the empirical Bayes model has a shrinkage pattern. The shrinkage
factor is estimated by using a Bayesian method with the regression
coefficients to be fixed at the maximum extended quasi-likelihood
estimates. This approach develops a Bayesian shrinkage estimate of the
mean which is numerically quite tractable. The method is illustrated with
a data set, and the estimate is compared with an earlier one based on an
empirical Bayes method. In a special case of the homogeneous model with
exchangeable priors, the performance of the Bayesian estimate is
illustrated by computer simulations. The simulation result shows as
improvement of the Bayesian estimate over the empirical Bayes estimate in
some situations.

*Key words and phrases*:
Bayes estimate, empirical Bayes,
extended quasi-likelihood, generalized linear model, relative saving
loss, shrinkage estimate.

**Source**
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