Publication Date

2019

Document Type

Dissertation/Thesis

First Advisor

Ryu, Duchwan

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Mathematical Sciences

Abstract

Functional Data Analysis (FDA) is a set of statistical methods that can deal with the data which represent curves or functions. In this dissertation, we consider two extensions of FDA to two types of data, circadian data and multidimensional data. The first part of the dissertation is concerned with the analysis of circadian data. We estimate circadian functions by using Bayesian smoothing splines under the generalized linear model, and extract two measures from each estimated function, magnitude and roughness. Based on extracted measures, we cluster individual functions into normal group and abnormal group by utilizing a density based clustering method. We examine the usability of the proposed measures through simulation studies and apply it to the analysis of physical daily activity in NHANES 2005-2006. The second part of this dissertation is concerned with the analysis of multidimensional data. We estimate multidimensional functions by using Bayesian P-splines within seemingly unrelated regression model (SUR). Based on the MCMC samples, we calculate dissimilarity measures between curves and cluster the curves in multidimensional space. We examine the usability of the proposed methodology through simulation studies and apply it to the analysis of brain neural activity data.

Extent

76 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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