# Meaning of “Uniformly” in UMP test and in UMVUE

What does the term "Uniformly" mean in UMP(Uniformly Most Powerful) test and in UMVUE(Uniformly Minimum Variance Unbiased Estimator)?

So far I have learnt, it means for all $$\theta$$(parameter). If it is, then for which $$\theta$$?

• Uniformly in these expressions means all over the parameter space, i.e., for all $\theta$'s. The domination of the UMP test or or the UMVU estimator over the competition is uniform in that there is no value of $\theta$ for which it does not occur. – Xi'an Oct 23 '20 at 5:35
• @Xi'an Can you please tell me for the UMP test- is it "for all $\theta$'s" for the Alternative hypothesis? If it is, then why? – n.u2877 Oct 23 '20 at 6:06
• I do not understand the question. The test $\varphi_0$ is UMP if its power is larger than the power of any other test, for all $\theta$'s. That is the definition of being UMP. So, why the "why"? – Xi'an Oct 23 '20 at 6:08
• I meant for which $\theta$. That is, the parameter space of the Null hypothesis or Alternative hypothesis? – n.u2877 Oct 23 '20 at 6:15