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Statistical Modeling of Multivariate...

Tidemann-Miller, Beth A.

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Statistical Modeling of Multivariate Functional Data that Exhibit Complex Correlation Structures.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Statistical Modeling of Multivariate Functional Data that Exhibit Complex Correlation Structures./
作者:	Tidemann-Miller, Beth A.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2014,
面頁冊數:	98 p.
附註:	Source: Dissertations Abstracts International, Volume: 76-07, Section: B.
Contained By:	Dissertations Abstracts International76-07B.
標題:	Biostatistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3647697
ISBN:	9781321414479

Statistical Modeling of Multivariate Functional Data that Exhibit Complex Correlation Structures.
Tidemann-Miller, Beth A.

Statistical Modeling of Multivariate Functional Data that Exhibit Complex Correlation Structures. - Ann Arbor : ProQuest Dissertations & Theses, 2014 - 98 p.

Source: Dissertations Abstracts International, Volume: 76-07, Section: B.

Thesis (Ph.D.)--North Carolina State University, 2014.

This item must not be sold to any third party vendors.

Due to the large size of modern data sets, there is an ever-increasing need for computationally efficient inferential methods designed for realistic models of large observed functional data sets. The first part of this dissertation introduces an innovative modeling framework for the analysis of multivariate functional data, where each individual functional component exhibits multilevel and spatial structures. The proposed methodology uses a functional principal components based approach for multivariate functional data, which has important advantages in the dimensionality reduction of the data and brings considerable computational savings. Moreover, our approach quantifies the spatial auto- and cross-correlation between units at the lowest level of the hierarchy. The proposed procedure is illustrated through simulation studies and data from a colon carcinogenesis experimental study. In the second part of the dissertation, we propose a Bayesian modeling framework for jointly analyzing multiple functional responses of different types (e.g. binary and continuous data). Our approach is based on a multivariate latent Gaussian process and models the dependence among the functional responses through the dependence of the latent process. Our framework easily accommodates additional covariates. We offer a way to estimate the multivariate latent covariance, allowing for implementation of multivariate functional principal components analysis to specify basis expansions and simplify computation. We demonstrate our method through both simulation studies and an application to real data from a periodontal study.

ISBN: 9781321414479Subjects--Topical Terms:

1002712
Biostatistics.
Subjects--Index Terms:

Binary and categorical functional responses

Statistical Modeling of Multivariate Functional Data that Exhibit Complex Correlation Structures.
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500 $a Source: Dissertations Abstracts International, Volume: 76-07, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Reich, Brian;Staicu, Ana-Maria.
502 $a Thesis (Ph.D.)--North Carolina State University, 2014.
506 $a This item must not be sold to any third party vendors.
520 $a Due to the large size of modern data sets, there is an ever-increasing need for computationally efficient inferential methods designed for realistic models of large observed functional data sets. The first part of this dissertation introduces an innovative modeling framework for the analysis of multivariate functional data, where each individual functional component exhibits multilevel and spatial structures. The proposed methodology uses a functional principal components based approach for multivariate functional data, which has important advantages in the dimensionality reduction of the data and brings considerable computational savings. Moreover, our approach quantifies the spatial auto- and cross-correlation between units at the lowest level of the hierarchy. The proposed procedure is illustrated through simulation studies and data from a colon carcinogenesis experimental study. In the second part of the dissertation, we propose a Bayesian modeling framework for jointly analyzing multiple functional responses of different types (e.g. binary and continuous data). Our approach is based on a multivariate latent Gaussian process and models the dependence among the functional responses through the dependence of the latent process. Our framework easily accommodates additional covariates. We offer a way to estimate the multivariate latent covariance, allowing for implementation of multivariate functional principal components analysis to specify basis expansions and simplify computation. We demonstrate our method through both simulation studies and an application to real data from a periodontal study.
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653 $a Binary and categorical functional responses
653 $a Bivariate functional data
653 $a Bivariate spatial modeling
653 $a Functional principal components analysis
653 $a Multivariate
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710 2 $a North Carolina State University. $3 1018772
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