On the admissibility and consistency of tests for homogeneity of variances
type: Item
instance of: scholarly article
title: On the admissibility and consistency of tests for homogeneity of variances
zbMATH Open document ID: 0691.62023
author: Arthur Cohen
author: John I. Marden
published in: The Annals of Statistics
publication date: 1989-01-01T00:00:00Z
review text: The authors consider the hypothesis testing problem for the homogeneity of variances in the one-way fixed and balanced analysis of variance model under the assumptions of independence and normality. They obtain a necessary and sufficient condition for admissibility of a test among the class of scale invariant tests. In particular they show that some classical tests such as Hartley's test and Cochran's test are not admissible. A certain limiting property (parameter consistency) of scale invariant tests is defined and it is shown that several well-known tests are parameter consistent for all significance levels. They also show that some well-known tests may not be parameter consistent or may be parameter consistent only for certain significance levels. Extensions to non-normal cases are also indicated.
reviewed by: Rasul A. Khan
Mathematics Subject Classification ID: 62F03
Mathematics Subject Classification ID: 62C15
Mathematics Subject Classification ID: 62F99
Mathematics Subject Classification ID: 62C07
Mathematics Subject Classification ID: 62J10
zbMATH DE Number: 4131437
zbMATH Keywords: maximal invariant parameter
zbMATH Keywords: Kullback-Leibler distance
zbMATH Keywords: likelihood ratio test
zbMATH Keywords: locally most powerful unbiased test
zbMATH Keywords: robust tests
zbMATH Keywords: homogeneity of variances
zbMATH Keywords: one-way fixed and balanced analysis of variance model
zbMATH Keywords: independence
zbMATH Keywords: normality
zbMATH Keywords: class of scale invariant tests
zbMATH Keywords: Hartley's test
zbMATH Keywords: Cochran's test
zbMATH Keywords: parameter consistency
zbMATH Keywords: significance levels
zbMATH Keywords: non-normal cases
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176347013
OpenAlex ID: W1981091429
DOI: 10.1214/AOS/1176347013
description: scientific article; zbMATH DE number 4131437