How do you know if a test is uniformly most powerful?
A test in class C, with power function β(θ), is a uniformly most powerful (UMP) class C test if β(θ) ≥ β′(θ) for every θ ∈ Θ0c and every β′(θ) that is a power function of a test in class C.
When do you use the likelihood ratio test?
The likelihood ratio test (LRT) is a statistical test of the goodness-of-fit between two models. A relatively more complex model is compared to a simpler model to see if it fits a particular dataset significantly better. If so, the additional parameters of the more complex model are often used in subsequent analyses.
When do you reject the likelihood ratio test?
Basically, the test compares the fit of two models. The null hypothesis is that the smaller model is the “best” model; It is rejected when the test statistic is large. In other words, if the null hypothesis is rejected, then the larger model is a significant improvement over the smaller one.
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 true value of the likelihood ratio?
The likelihood ratio test is based on the likelihood function fn(X¡1;¢¢¢;Xnjµ), and the intuition that the likelihood function tends to be highest near the true value of µ. Indeed, this is also the foundation for maximum likelihood estimation.
Who is the instructor for the likelihood ratio test?
Instructor: Songfeng Zheng. A very popular form of hypothesis test is the likelihood ratio test, which is a generalization of the optimal test for simple null and alternative hypotheses that was developed by Neyman and Pearson (We skipped Neyman-Pearson lemma because we are short of time).
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\\).