Most Powerful Invariant Tests for Binormality

Uniformly Most Powerful Bayesian Tests.

Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the Bayesian setting by defining uniformly most powerful Bayesian tests to be tests that maximize the probability that the Bayes factor, in favor of the alternat...

The behavior of locally most powerful tests

The locally most powerful (LMP) tests of the hypothesis H : 6 = 6Q against one-sided as well as two-sided alternatives are compared with several competitive tests, as the likelihood ratio tests, the Wald-type tests and the Rao score tests, for several distribution shapes and for location, shape and vector parameters. A simulation study confirms the importance of the condition of local unbiasedn...

UNIFORMLY MOST POWERFUL BAYESIAN TESTS By Valen

Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the Bayesian setting by defining uniformly most powerful Bayesian tests to be tests that maximize the probability that the Bayes factor, in favor of the alternat...

Lecture 10 slides: Uniformly most powerful tests

Let Θ = Θ0 ∪Θ1 be a parameter space. Consider a parametric family {f(x|θ), θ ∈ Θ}. Suppose we want to test the null hypothesis, H0, that θ ∈ Θ0 against the alternative, Ha, that θ ∈ Θ1. Let C be some critical set. Then the probability that the null hypothesis is rejected is given by β(θ) = Pθ{X ∈/ C}. Recall that the test based on C has level α if α ≥ supθ Θ0 β(θ). The restriction of β(·) on Θ1...

Some Locally Most Powerful Rank Tests For Correlation