Complete statistic
= Complete statistic
{title2=$\mathbb E_\theta g(T)=0\ \forall\theta\Longrightarrow g(T)=0\text{ a.s. for all }\theta$}
= Completeness of a statistic
{synonym}
A statistic is complete for a parameter family if the displayed implication holds for every measurable $g$ integrable under all parameter values. This property does not itself assert sufficiency; a <complete sufficient statistic> has both properties. A nonconstant unbiased estimator of a known constant provides a direct obstruction to completeness.