I am trying to derive an variance estimator $var(\hat{\theta}(\mu,x))$ for an point estimator $\hat{\theta}(\mu,x)$, where $\mu$ is the true mean, $x$ is the data.
Now I need to replace the true mean $\mu$ with the sample mean $\hat{\mu}$. Then what is the general approach to incorporate this extra variability of sample mean $\hat{\mu}$ in computing $var(\hat{\theta}(\mu,x))$?
Any reference, comment or suggestion will be appreciated!