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Asymptotic Theory for Linear Mixed Effects Models With Large Cluster Size

Lyu, Ziyang

Description

This thesis first deals with asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model when both the number of independent clusters and the cluster sizes (the number of observations in each cluster) go to infinity. A set of conditions is given under which the estimators are shown to be asymptotically normal. There are no restrictions on the rate at which the cluster size tends to infinity. Moreover,...[Show more]

dc.contributor.authorLyu, Ziyang
dc.date.accessioned2020-06-05T04:08:58Z
dc.date.available2020-06-05T04:08:58Z
dc.identifier.urihttp://hdl.handle.net/1885/204854
dc.description.abstractThis thesis first deals with asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model when both the number of independent clusters and the cluster sizes (the number of observations in each cluster) go to infinity. A set of conditions is given under which the estimators are shown to be asymptotically normal. There are no restrictions on the rate at which the cluster size tends to infinity. Moreover, this thesis deals with the estimated distributions of the estimated best linear unbiased predictors (EBLUP) of the random effects, with ML/REML, estimated variance components, converge to the true distributions of the corresponding random effects, when both of the number of independent clusters and the cluster sizes (the number of observations in each cluster) go to infinity.
dc.language.isoen_AU
dc.titleAsymptotic Theory for Linear Mixed Effects Models With Large Cluster Size
dc.typeThesis (PhD)
local.contributor.supervisorWelsh, Alan
local.contributor.supervisorcontactu8204947@anu.edu.au
dc.date.issued2020
local.contributor.affiliationMathematical Science Institute, ANU College of Science, The Australian National University
local.identifier.doi10.25911/5eeb43c1a5614
local.identifier.proquestYes
local.thesisANUonly.author59ee4dac-aa5e-48fa-8df5-a20ecedd7cb3
local.thesisANUonly.title000000014940_TC_1
local.thesisANUonly.keycf6adfe5-cbc5-b3bb-e055-b1c092be59af
local.mintdoimint
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