New methods and models in functional data analysis

Author: 
Date created: 
2018-07-23
Identifier: 
etd19690
Keywords: 
Functional data analysis
Functional principal component analysis
Dynamical correlation
Sparse
Semiprametric additive models
Quantile regression
Abstract: 

Functional data analysis (FDA) plays an important role in analyzing function-valued data such as growth curves, medical images and electromagnetic spectrum profiles, etc. Since dimension reduction can be achieved for infinite-dimensional functional data via functional principal component analysis (FPCA), this technique has attracted substantial attention. We develop an easy-to-implement algorithm to perform FPCA and find that this algorithm compares favorably with traditional methods in numerous applications. Knowing how ran- dom functions interact is critical to studying mechanisms like gene regulations and event- related brain activation. A new approach is proposed to calibrate dynamical correlations of random functions and we apply this approach to quantify functional connectivity from medical images. Scalar-on-function regression, which is widely used to characterize the re- lationship between a functional covariate and a scalar response, is an important ingredient of FDA. We propose several new scalar-on-function regression models and investigate their properties from both theoretical and practical perspectives.

Document type: 
Thesis
Rights: 
This thesis may be printed or downloaded for non-commercial research and scholarly purposes. Copyright remains with the author.
File(s): 
Senior supervisor: 
Jiguo Cao
Department: 
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Thesis) Ph.D.
Statistics: