Uniformly Minimum-Variance Unbiased Estimator

Topics: Statistics - Cramér-Rao Lower Bound

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(theorem)

Let $T$ be an estimator of $\theta$ (a parameter).

If $T$ is (1) unbiased for $\theta$ and (2) $\mathrm{Var}(T)=\mathrm{CRLB}(\theta )$ (see Cramér-Rae lower bound), then $T$ is a uniformly minimum-variance unbiased estimator (UMVUE).