Is the generalized likelihood ratio test uniformly most powerful?
For testing a one-sided hypothesis in a one-parameter family of distributions, it is shown that the generalized likelihood ratio (GLR) test coincides with the uniformly most powerful (UMP) test, assuming certain monotonicity properties for the likelihood function.
What does it mean to say that the considered likelihood ratio test is the uniformly most powerful test?
In statistical hypothesis testing, a uniformly most powerful (UMP) test is a hypothesis test which has the greatest power. among all possible tests of a given size α. For example, according to the Neyman–Pearson lemma, the likelihood-ratio test is UMP for testing simple (point) hypotheses.
When is a test called a uniformly most powerful test?
A test defined by a critical region C of size α is a uniformly most powerful (UMP) test if it is a most powerful test against each simple alternative in the alternative hypothesis H A. The critical region C is called a uniformly most powerful critical region of size α.
Which is the most powerful test in the world?
A test defined by a critical region Cof size \\(\\alpha\\) is a uniformly most powerful (UMP) testif it is a most powerful test against each simple alternative in the alternative hypothesis \\(H_A\\). The critical region Cis called a uniformly most powerful critical region of size \\(\\alpha\\).
Is the Neyman Pearson lemma a uniformly most powerful test?
The good news is that we can extend the Neyman Pearson Lemma to account for composite alternative hypotheses, providing we take into account each simple alternative specified in H_A. Doing so creates what is called auniformly most powerful(or UMP) test. Uniformly Most Powerful (UMP) test
Which is the uniformly most powerful critical region?
The critical region C is called a uniformly most powerful critical region of size α. Let’s demonstrate by returning to the normal example from the previous page, but this time specifying a composite alternative hypothesis.