= Uniform minimum variance conditionally unbiased estimator
{title2=$\mathbb E_\theta(\widehat\theta\mid C)=\theta$}
= UMVCUE
{c}
{synonym}
A UMVCUE has minimum conditional <variance> among all <estimators> unbiased in the selected experiment for every parameter. For independent Gaussian stage estimates $A,V$ with information $I_1,J$, continuation $A\geq c$, total information $I_2=I_1+J$ and pooled estimate $T$, <Rao-Blackwellization> of the fresh estimate gives $T-(I_1s/J)\phi((T-c)/s)/\Phi((T-c)/s)$, where $s^2=1/I_1-1/I_2$. The conditional family has <complete sufficient statistic> $T$, so the <Lehmann–Scheffé theorem> establishes the optimum. A conditional-<likelihood> bias correction does not automatically have this unbiasedness property.
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