Complete Statistic

Definition

Let $Z$ be a Random Variable with PDF $h(z|\theta )$, where $\theta \in \Omega$. A complete statistic $Z$ for $\theta$ satisfies the condition $\forall \theta \in \Omega ,E[u(Z)]=0\Rightarrow u(Z)=0$ then, $\{h(z|\theta )|\theta \in \Omega \}$ is called a complete family.