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