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Joint Mean and Covariance Modeling of Matrix-Variate Data

dc.contributor.authorHornstein, Michael
dc.date.accessioned2018-10-25T17:40:13Z
dc.date.availableNO_RESTRICTION
dc.date.available2018-10-25T17:40:13Z
dc.date.issued2018
dc.date.submitted2018
dc.identifier.urihttps://hdl.handle.net/2027.42/145953
dc.description.abstractThis dissertation addresses theory, methodology, and applications for joint mean and covariance estimation with matrix-variate data. Chapters 2 and 3 consider joint mean and covariance estimation in the Kronecker product model, which has natural methodological connections to large-scale screening and differential mean analysis in various application areas including genomics. It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated high-dimensional data with unknown mean and dependence structures. Matrix-variate approaches that impose various forms of (inverse) covariance sparsity allow flexible dependence structures to be estimated, but cannot directly be applied when the mean and covariance matrices are estimated jointly. We present a practical method utilizing generalized least squares and penalized (inverse) covariance estimation to address this challenge. We establish consistency and obtain rates of convergence for estimating the mean parameters and covariance matrices. The advantages of our approaches are: (i) dependence graphs and covariance structures can be estimated in the presence of unknown mean structure, (ii) the mean structure becomes more efficiently estimated when accounting for the dependence structure among observations; and (iii) inferences about the mean parameters become correctly calibrated. We use simulation studies and analysis of genomic data from a twin study of ulcerative colitis to illustrate the statistical convergence and the performance of our methods in practical settings. Several lines of evidence show that the test statistics for differential gene expression produced by our methods are correctly calibrated and improve power over conventional methods. Chapter 4 uses matrix-variate techniques to gain insight into pitch curve data that plays an important role in linguistics research. These curves can be viewed as large multi-indexed data arrays with distinct covariance behaviors along each index. We estimate covariance and inverse covariance matrices and graphs, and we connect edge structures to word properties.
dc.language.isoen_US
dc.subjecttwo-group comparison
dc.subjectsparsity
dc.subjectgenomics
dc.subjectgeneralized least squares
dc.subjectgraphical modeling
dc.subjectphonetics pitch curves
dc.titleJoint Mean and Covariance Modeling of Matrix-Variate Data
dc.typeThesisen_US
dc.description.thesisdegreenamePhDen_US
dc.description.thesisdegreedisciplineStatistics
dc.description.thesisdegreegrantorUniversity of Michigan, Horace H. Rackham School of Graduate Studies
dc.contributor.committeememberShedden, Kerby A
dc.contributor.committeememberZhou, Shuheng
dc.contributor.committeememberRichstone, Douglas O
dc.contributor.committeememberHero III, Alfred O
dc.subject.hlbsecondlevelMathematics
dc.subject.hlbsecondlevelStatistics and Numeric Data
dc.subject.hlbtoplevelHealth Sciences
dc.subject.hlbtoplevelScience
dc.subject.hlbtoplevelSocial Sciences
dc.description.bitstreamurlhttps://deepblue.lib.umich.edu/bitstream/2027.42/145953/1/mdhorn_1.pdf
dc.identifier.orcid0000-0003-2721-807X
dc.identifier.name-orcidHornstein, Michael; 0000-0003-2721-807Xen_US
dc.owningcollnameDissertations and Theses (Ph.D. and Master's)


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