Let $X_1, \cdots, X_n$ be iid from a uniform distribution $U[-\theta, 2\theta]$ with $\theta \in \mathbb{R}^+$ unknown. Check if the minimal sufficient statistic of $\theta$ is complete.
I found that$$T(X) = \max \left(-X_{(1)}, \frac{X_{(n)}}{2} \right)$$is minimal sufficient but i am having trouble checking if it's complete.
My attempt: Since uniform is a location distribution, using Basu's theorem, the ancillary statistic would be the range. Since the above minimal statistic is not independent of the ancillary statistic, it is not complete. Am I right?