As a branch of statistics, functional data analysis (FDA) studies observations
regarded as curves, surfaces, or other objects evolving over a continuum. Although
one has seen a flourishing of methods and theories on FDA, two issues
are observed. Firstly, the functional data are sampled from common time grids;
secondly, methods developed only for univariate functional data are challenging
to be applied to multivariate functional data. After exploring model-based fitting
for regularly observed multivariate functional data, we explore new visualization
tools, clustering, and multivariate functional depths for irregularly observed
(sparse) multivariate functional data. The four main chapters that comprise the
dissertation are organized as follows. First, median polish for functional multivariate
analysis of variance (FMANOVA) is proposed with the implementation of
multivariate functional depths in Chapter 2. Numerical studies and environmental
datasets are considered to illustrate the robustness of median polish. Second, the
sparse functional boxplot and the intensity sparse functional boxplot, as practical
exploratory tools that make visualization possible for both complete and sparse
functional data, are introduced in Chapter 3. These visualization tools depict
sparseness characteristics in the proportion of sparseness and relative intensity
of fitted sparse points inside the central region, respectively. Third, a robust
distance-based robust two-layer partition (RTLP) clustering of sparse multivariate
functional data is introduced in Chapter 4. The RTLP clustering is based
on our proposed elastic time distance (ETD) specifically for sparse multivariate
functional data. Lastly, the multivariate functional integrated depth and the multivariate
functional extremal depth based on multivariate depths are proposed in
Chapter 5. Global and local formulas for each depth are explored, with theoretical
properties being proved and the finite sample depth estimation for irregularly
observed multivariate functional data being investigated. In addition, the simplified
sparse functional boxplot and simplified intensity sparse functional boxplot for
visualization without data reconstruction are introduced. Together, these four
extensions to multivariate functional data make them more general and of applicational
interest in exploratory multivariate functional data analysis.
| Identifer | oai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/686099 |
| Date | 11 1900 |
| Creators | Qu, Zhuo |
| Contributors | Genton, Marc G., Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division, Ombao, Hernando, Alouini, Mohamed-Slim, Shang, Hanlin |
| Source Sets | King Abdullah University of Science and Technology |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Rights | 2023-12-01, At the time of archiving, the student author of this dissertation opted to temporarily restrict access to it. The full text of this dissertation will become available to the public after the expiration of the embargo on 2023-12-01. |
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