Ancillary Statistic

Definition

Let $X_1,X_2,\dots ,X_n$ be a Random Sample with PDF $f(x|\theta )$, where $\theta \in \Omega$ $Y_1=u_1(X_1,X_2,\dots ,X_n)$ is called ancillary statistic to $\theta$ if its distribution does not depend on the $\theta$