= Boundedly complete statistic
= Boundedly complete
{synonym}
= Bounded completeness of a statistic
{synonym}
Bounded completeness requires the defining implication for a <complete statistic> only for bounded measurable functions. Completeness implies it, but the converse need not hold. If a <sufficient statistic> $T$ gives a parameter-independent event probability $c$ and the conditional probability $S(T)$ of that event is nonconstant, then $S-c$ is a bounded zero-mean obstruction to bounded completeness.
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