Date of Award

6-2024

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Hyun Bin Kang, Ph.D.

Second Advisor

Joshua Naranjo, Ph.D.

Third Advisor

Kevin Lee, Ph.D.

Fourth Advisor

Sangwoo Lee, Ph.D.

Keywords

Functional data analysis (FDA), functional generalized linear mixed model (FGLMM), Monte Carlo method, quasi-likelihood

Abstract

Functional Data Analysis (FDA) is a topic of growing interest in the statistics community and is applied in a wide range of fields such as Anthropology, Epidemiology, Meteorology, Neurology and Engineering. The data in FDA are smooth curves or surfaces in time or space which can be conceptualized as functions. Because of the smooth nature of the data and the measurements are highly correlated, making the classical methods such as univariate or multivariate analysis are infeasible for such data. Functional data Analysis (FDA) deals with these kinds of more detailed, complex, and structured data.

In this dissertation, we propose a Functional Generalized Linear Mixed Model (FGLMM), which extends the traditional Generalized Linear Mixed models (GLMM) framework to incorporate functional covariates. Our model addresses scenarios involving non-Gaussian scalar responses, functional predictors, and random effects. Unlike conventional GLMM, our model relaxes the assumptions regarding link and variance functions and estimates them nonparametrically from the data. The model allows the analysis of higher-dimensional datasets, which are often encountered in contemporary research settings. We use Quasi-likelihood procedure and Monte Carlo Method for estimation in FGLMM.

Understanding the intricate characteristics of brain waveforms and rhythms during various cognitive tasks and relaxation states has been a topic of interest in scientific communities. We apply our proposed model to analyze the observed brainwaves while watching videos and the associated confusion levels and the associated confusion levels to gain insights into cognitive processes.

Access Setting

Dissertation-Open Access

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