Complete class results for hypothesis testing problems with simple null hypotheses
type: Item
instance of: scholarly article
title: Complete class results for hypothesis testing problems with simple null hypotheses
zbMATH Open document ID: 0685.62008
author: Lawrence Brown
author: John I. Marden
published in: The Annals of Statistics
publication date: 1989-01-01T00:00:00Z
review text: This paper deals with the characterization of admissibility for the testing of hypotheses, where the null hypothesis is simple, the parameter space is finite dimensional and the supports of the probability distributions do not depend on the parameter. Essentially complete class results are given for characterizing the limits of Bayes tests. Conditions for tests to be admissible and the class to be complete are given. The given results are specialized to the exponential families with illustrative examples: testing the correlation is 0 in a bivariate normal distribution when the means and variances are known, testing the location parameter of the shifted double exponential distribution is 0, and testing that a bivariate normal distribution has zero means versus the alternative that one mean is at least as large as the other in absolute value.
Mathematics Subject Classification ID: 62C07
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62F05
Mathematics Subject Classification ID: 62C10
zbMATH DE Number: 4123043
zbMATH Keywords: simple hypotheses
zbMATH Keywords: invariant tests
zbMATH Keywords: characterization of admissibility
zbMATH Keywords: Essentially complete class results
zbMATH Keywords: limits of Bayes tests.
zbMATH Keywords: exponential families
zbMATH Keywords: correlation
zbMATH Keywords: bivariate normal distribution
zbMATH Keywords: shifted double exponential distribution
reviewed by: Khursheed Alam
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176347012
OpenAlex ID: W1997272527
DOI: 10.1214/AOS/1176347012
description: scientific article; zbMATH DE number 4123043