Date of Award

6-1-2023

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Hyun Bin Kang, Ph.D.

Second Advisor

Joshua Naranjo, Ph.D.

Third Advisor

Duy Ngo, Ph.D.

Fourth Advisor

Sangwoo Lee, Ph.D.

Abstract

With the advancements in data collection technologies, researchers in various fields such as epidemiology, chemometrics, and environmental science face the challenges of obtaining useful information from more detailed, complex, and intricately-structured data. Since the existing methods often are not suitable for such data, new statistical methods are developed to accommodate the complicated data structures.

As a part of such efforts, this dissertation proposes Functional Generalized Linear Mixed Model (FGLMM), which extends classical generalized linear mixed models to include functional covariates. Functional Data Analysis (FDA) is a rapidly developing area of statistics for data which can be naturally viewed as smooth curves or functions. FDA methods exploit the natural smoothness that characterizes the data and achieves greater statistical efficiency compared to multivariate methods.

After introducing the FGLMM, parameter estimation methods using both Frequentist and Bayesian approaches are discussed. The simulation settings of a random intercept model are used to show the performance of the two estimation schemes. Also, the higher prediction performance of FGLMM will be shown compared to the Functional Generalized Linear Model (FGLM) and the Generalized Linear Mixed Model (GLMM). Also, an application of the FGLMM to EEG brainwave data is discussed.

Access Setting

Dissertation-Open Access

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