On the multivariate components of variance problem

dc.contributor.advisor Yasuo Amemiya
dc.contributor.author Remadi, Sellem
dc.contributor.department Statistics
dc.date 2018-08-23T13:11:26.000
dc.date.accessioned 2020-06-30T07:04:03Z
dc.date.available 2020-06-30T07:04:03Z
dc.date.copyright Wed Jan 01 00:00:00 UTC 1992
dc.date.issued 1992
dc.description.abstract <p>Statistical procedures for making inferences on the variance components in univariate mixed effect models have been developed and extensively used in many fields. Development for multivariate mixed models has been relatively limited. One important issue in the multivariate problem is determining the rank of a covariance component. Testing for the rank can be considered a natural extension of the univariate problem of testing for the existence of a random effect. Knowledge on the rank can be utilized to obtain efficient estimators. Also, the true unknown rank of a covariance component influences properties of estimators of this and other covariance components. This issue on the rank is one of the underlying themes throughout this dissertation. A difficulty in developing asymptotic inference procedures for the general random effect problem is the nonexistence of a single index over which the limit is taken. For example, a one-way model has two indices, the numbers of groups and replicates. In order to develop inference procedures useful for various practical situations, asymptotic theory has to be developed under correspondingly various conditions. An eventual goal of this dissertation is to develop approximate inference procedures which can be justifiably used for a wide range of practical sampling configurations;To develop asymptotic theory, a certain nonstandard result on the limiting distribution of the roots of a determinantal equation is needed. The first paper of this dissertation presents general results on such a limiting distribution. The second paper deals with the rank testing problem. A number of asymptotic and exact procedures are discussed for a large class of multivariate mixed effect models. Practical testing procedures which can be used under various sampling configurations are derived. The third paper discusses asymptotic properties of the covariance component estimators in the multivariate one-way random effect model with possibly incorrect specification of the rank of the between-group component. Approximate inference procedures for covariance components which are useful for most practical situations are proposed.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/rtd/10343/
dc.identifier.articleid 11342
dc.identifier.contextkey 6399851
dc.identifier.doi https://doi.org/10.31274/rtd-180813-9663
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/10343
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/63479
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/rtd/10343/r_9234846.pdf|||Fri Jan 14 18:19:06 UTC 2022
dc.subject.disciplines Statistics and Probability
dc.subject.keywords Statistics
dc.title On the multivariate components of variance problem
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 264904d9-9e66-4169-8e11-034e537ddbca
thesis.degree.level dissertation
thesis.degree.name Doctor of Philosophy
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