Uniformly minimum variance unbiased estimator

Definition

An estimator $\hat{\theta }$ is called UMVUE if

• $\hat{\theta }$ is an unbiased estimator and
• For any other unbiased estimator ${\hat{\theta }}^{\ast }$, $V(\hat{\theta })\le V({\hat{\theta }}^{\ast })$ for $\forall {\hat{\theta }}^{\ast }\in \Omega$.

Sometimes we can come up with a lower bound such that any unbiased estimator having it’s variance equal to that bound would be the UMVUE.

One of such bounds is Crame’r-Rao lower bound.