Uniformly more powerful tests for hypotheses about linear inequalities when the variance is unknown

Uniformly More Powerful, One-sided Tests for Hypotheses about Linear Inequalities

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...

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...

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...

Mixing least-squares estimators when the variance is unknown

We propose a procedure to handle the problem of Gaussian regression when the variance is unknown. We mix least-squares estimators from various models according to a procedure inspired by that of Leung and Barron [IEEE Trans. Inform. Theory 52 (2006) 3396–3410]. We show that in some cases, the resulting estimator is a simple shrinkage estimator. We then apply this procedure to perform adaptive e...