Decision Function

Definition

Let $X_1,X_2,\dots ,X_n$ be Random Sample with PDF $f(x|\theta )$, where $\theta \in \Omega$, $X:=u(X_1,X_2,\dots ,X_n)$ be a Statistic for the parameter $\theta$, and $\delta (x)$ be a function of the observed value of the statistic $X$, then The function $\delta$ is called a decision function or a decision rule.