Among unbiased estimators, there often exists one with the lowest variance, called the minimum variance unbiased estimator (MVUE).

Thus e(T) is the minimum possible variance for an unbiased estimator divided by its actual variance.

The maximum-likelihood estimate is unbiased, with minimum variance, so it is a good estimate to use.

These are known to be the uniformly minimum variance unbiased (UMVU) estimators for the continuous uniform distribution.

"Best" means that the least squares estimators of the parameters have minimum variance.

The difference between the treatment and the control can thus be given minimum variance (i.e. maximum precision) by maximising the covariance (or the correlation) between X and Y.

Such a solution achieves the lowest possible mean squared error among all unbiased methods, and is therefore the minimum variance unbiased (MVU) estimator.

As we're restricting to unbiased estimators, minimum mean squared error implies minimum variance.

"Unbiased statistics with minimum variance", Proc.

An approximately unbiased estimator, with minimum variance for large values of n, with a bias of order , can be obtained by maximizing , i.e. .