Minimum Variance Unbiased Estimator (MVUE)

Definition

Let

• $X_1,\dots ,X_n$ : Random sample
• $Y=u(X_1,\dots ,X_n)$ : Statistic
• $\theta$ : Parameter

If

• $Y$ : Unbiased estimator of $\theta$
• $\mathrm{Var}(Y)$ is lower than every other unbiased estimator of $\theta$

Then $Y$ is the mininum variance unbiased estimator (MVUE) of $\theta$

Remark

We usually use Lehmann and Scheffe Theorem to prove that a statistic is MVUE.