Efficiency

Suppose that both estimators \({\hat{\theta}}_1\) and \({\hat{\theta}}_2\) are non-biassed, then we will say that \({\hat{\theta}}_1\) is more effective than \({\hat{\theta}}_2\) if

\(Var\left[{\hat{\theta}}_1\right]\ <\ Var\left[{\hat{\theta}}_2\right]\)

Thus, among the class of \(\theta\)-free estimators, the minimal variance non-biassed estimator is the one with the smallest variance.