Statistical Methods for Non-Linear Modeling in Functional Data
Open Access
Author:
Rao, Aniruddha Rajendra
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 17, 2021
Committee Members:
Lin Lin, Major Field Member Suhang Wang, Outside Unit & Field Member Jia Li, Major Field Member Matthew Reimherr, Chair & Dissertation Advisor Ephraim Hanks, Program Head/Chair
Keywords:
Functional Data Neural Network Deep Learning Non-Linear Modeling Imputation
Abstract:
In Functional Data Analysis (FDA), functional regression can mainly be classified into three major categories according to the role played by the functional data in each model: scalar response and functional predictors (scalar-on-function regression); functional response and scalar predictors (function-on-scalar regression); and functional response and functional predictors (function-on-function regression). Even though Functional Regression is perhaps one of the most thoroughly researched topics within the broader literature on FDA, there is still a great need for superior non-linear models. In this dissertation, we have developed methods to deal with complex non-linear relations in functional data under different settings, including (1) Imputation, (2) Spatial dependency, (3) scalar-on-function modeling, and (4) function-on-function modeling.
