Ancillary Statistic

Def: A statistic $T(\underset{―}{X})$ is which distribution doesn't depend on the parameter $\theta$, it is called an ancillary statistic.

Some ancillary statistics, are

• the range of sample
• sample variance

Basu Theorem

If $S(\underset{―}{X})$ is a sufficient and complete statistic, and $T(\underset{―}{X})$ is an ancillary statistic, then $S(\underset{―}{X})$ and $T(\underset{―}{X})$ are independent.