Show that for testing the hypothesis $H_{0}: \theta_{1} \leq \theta \leq \theta_{2}$ versus $H_{1}: \theta<\theta_{1}$ or $\theta>\theta_{2}$,or the hypothesis $H_{0}:\theta=\theta_{0}$ versus $H_{1}: \theta\ne\theta_{0}$ in the one-parameter exponential family ,the UMP tests do not exist.
We can find some specific examples to show that the UMP tests fail to exist.In general,how to proof the UMP tests do not exist theoretically ? I think proof it by contradiction will come into play likewise specific cases,are there some suggestions to construct the conflict?