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Science Forum Index » Statistics - Math Forum » Bayesian statistics and sufficient statistics...
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 Posted: Wed Jul 02, 2008 4:55 am |
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Guest
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Hi everyone,
I am working on the following question: Suppose that T is a sufficient
statistic for unknown parameter theta, based on a sample X.
a)Prove that the Bayes estimator db(X) of theta is a function of T.
b)Under what conditions can you construct a UMVUE estimate of theta
which is a function of db(X).
The following is my work so far.
a)The posterior distribution theta|X is the same as theta|T since
theta|X
is proportional to
X|theta*theta
=
X|T,theta*T|theta*theta
is proportional to
T|theta*theta
where the last line uses the sufficiency of T
b)We know from a) that db(X) of theta is a function of T. We also need
that db(X) is complete.
Am I right? What can I do to improve my arguments?
I appreciate your help. |
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