Sufficient statistic for a symmetric uniform sample
= Sufficient statistic for a symmetric uniform sample
{title2=$M=\max_i|X_i|$}
For independent samples uniform on $[-\theta,\theta]$ with $\theta>0$, the absolute maximum $M$ is a <minimal sufficient statistic>, since the likelihood is $(2\theta)^{-n}\mathbf1_{\{\theta\geq M\}}$. The pair of sample minimum and maximum is a <sufficient statistic> but is not minimal: simultaneous sign reversal preserves $M$ and generally changes that pair.