The Expected Sample Variance of Uncorrelated Random Variables with a Common Mean and Some Applications in Unbalanced Random Effects Models

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dc.contributor.author Vardeman, Stephen
dc.contributor.author Wendelberger, Joanne
dc.contributor.author Vardeman, Stephen
dc.contributor.department Statistics
dc.contributor.department Industrial and Manufacturing Systems Engineering
dc.date 2018-02-17T14:02:05.000
dc.date.accessioned 2020-07-02T06:57:59Z
dc.date.available 2020-07-02T06:57:59Z
dc.date.copyright Sat Jan 01 00:00:00 UTC 2005
dc.date.issued 2005-03-01
dc.description.abstract <p>There is a little-known but very simple generalization of the standard result that for uncorrelated random variables with common mean µ and variance 2 σ , the expected value of the sample variance is 2 σ . The generalization justifies the use of the usual standard error of the sample mean in possibly heteroscedastic situations, and motivates elementary estimators in even unbalanced linear random effects models. The latter both provides nontrivial examples and exercises concerning method-of-moments estimation, and also helps "demystify" the whole matter of variance component estimation. This is illustrated in general for the simple one-way context and for a specific unbalanced two-factor hierarchical data structure.</p>
dc.description.comments <p>This article is from <em>Journal of Statistics Education</em> 13 (2005): <a href="http://www.amstat.org/publications/jse/v13n1/vardeman.html" target="_blank">www.amstat.org/publications/jse/v13n1/vardeman.html</a></p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/stat_las_pubs/65/
dc.identifier.articleid 1064
dc.identifier.contextkey 8243998
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath stat_las_pubs/65
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/90665
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/stat_las_pubs/65/0-2005_Journal_of_Statistics_Education_permission.pdf|||Sat Jan 15 01:23:35 UTC 2022
dc.source.bitstream archive/lib.dr.iastate.edu/stat_las_pubs/65/2005_VardemanSB_ExpectedSampleVariance.pdf|||Sat Jan 15 01:23:36 UTC 2022
dc.source.uri 10.17877/DE290R-7656
dc.subject.disciplines Statistics and Probability
dc.subject.keywords Heteroscedastic
dc.subject.keywords Method of moments
dc.subject.keywords One-way model
dc.subject.keywords Two-factor hierarchical model
dc.subject.keywords Standard error of the mean
dc.subject.keywords Variance component
dc.title The Expected Sample Variance of Uncorrelated Random Variables with a Common Mean and Some Applications in Unbalanced Random Effects Models
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isAuthorOfPublication d398ec8c-7612-4286-b7b8-88f844f10410
relation.isOrgUnitOfPublication 264904d9-9e66-4169-8e11-034e537ddbca
relation.isOrgUnitOfPublication 51d8b1a0-5b93-4ee8-990a-a0e04d3501b1
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