Functional data refer to data which consist of observed functions or curves evaluated
at a finite subset of some interval. In this dissertation, we discuss statistical
analysis, especially classification and regression when data are available in function
forms. Due to the nature of functional data, one considers function spaces in presenting
such type of data, and each functional observation is viewed as a realization
generated by a random mechanism in the spaces. The classification procedure in
this dissertation is based on dimension reduction techniques of the spaces. One commonly
used method is Functional Principal Component Analysis (Functional PCA) in
which eigen decomposition of the covariance function is employed to find the highest
variability along which the data have in the function space. The reduced space of
functions spanned by a few eigenfunctions are thought of as a space where most of the
features of the functional data are contained. We also propose a functional regression
model for scalar responses. Infinite dimensionality of the spaces for a predictor causes
many problems, and one such problem is that there are infinitely many solutions. The
space of the parameter function is restricted to Sobolev-Hilbert spaces and the loss
function, so called, e-insensitive loss function is utilized. As a robust technique of
function estimation, we present a way to find a function that has at most e deviation
from the observed values and at the same time is as smooth as possible.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/2805 |
| Date | 01 November 2005 |
| Creators | Lee, Ho-Jin |
| Contributors | Hsing, Tailen |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 1204455 bytes, electronic, application/pdf, born digital |
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