A minimum variance unbiased estimator of a real parameter 
is an unbiased estimator 
with finite variance that has the smallest variance
among all unbiased estimators based on the
same observations for every admissible value of 
(Lehmann and Casella 1998). Thus, for any other unbiased
estimator 
of 
,
 |
where the subscript indicates the value of the parameter at which the variance is evaluated.
The German tank problem provides an example. A minimum variance unbiased estimator need not exist for every estimation problem.
