Let $X_1, ..., X_n$ be a random sample from the $N(\theta,1)$ distribution. Find a minimal sufficient statistic for $\theta$.
Now, I can find a sufficient statistic using the factorisation theorem ($\sum X_i$), but I don't think that this statistic is in fact minimal sufficient.
The question seems to imply that there exists a minimal sufficient statistic, but I'm not even sure that there is one.
MY QUESTION: How would I go about proving that there is no minimal sufficient statistic, or if there is one, what is it!?
Any hints greatly appreciated!