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LINEAR BAYES AND OPTIMAL ESTIMATION

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V. P. GODAMBE

*Department of Statistics and Actuarial Science, University of Waterloo,*

Waterloo, Ontario, Canada N2L 3G1
(Received August 26, 1996; revised September 8, 1997)

**Abstract.**
In non-Bayesian statistics, it is often
realistic to replace a full distributional assumption by a
much weaker assumption about its first few moments; such as
for instance, mean and variance. Along the same lines in
Bayesian statistics one may wish to replace a completely
specified prior distribution by an assumption about just a
few moments of the distribution. To deal with such Bayesian
semi-parametric models defined only by a few moments,
Hartigan (1969, *J. Roy. Statist. Soc. Ser. B*,
**31**, 440-454) put forward linear Bayes methodology.
By now it has become a standard tool in Bayesian analysis. In
this paper we formulate an alternative methodology based on
the theory of optimum estimating functions. This alternative
methodology is shown to be more readily applicable and
efficient in common problems, than the linear Bayes
methodology mentioned above.

*Key words and phrases*:
Bayes methodology,
conditioning, estimating functions, linearity, optimality.

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