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Let $X $ be observed data. Let $\hat{\theta}(X)$ be an unbiased estimate of $\theta$ and let T be a sucient statistic for $\theta$. Define the new estimator $\hat\theta^{*}$ of $\theta$,

$$ \hat\theta^{*}(X) =E(\hat\theta(X)| T) $$

Then, show that:

$ \hat\theta^{*}(X)$ is unbiased

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Use that in general: $E[E[X\mid Y]]=E[X]$ whatever $X$ and $Y$ may be (such that the conditional expectation exists). –  Stefan Hansen Sep 30 '12 at 14:59
    
related to math.stackexchange.com/questions/204890/… –  Henry Sep 30 '12 at 15:50
    

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