Many common clustering methods cannot be used for clustering multivariate longitudinal data when the covariance of random variables is a function of the time points. For this reason, a copula kernel mixture model (CKMM) is proposed for clustering such data. The CKMM is a finite mixture model that decomposes each mixture component’s joint density function into a copula and marginal distribution functions, where a Gaussian copula is used for its mathematical traceability. This thesis considers three scenarios: first, the CKMM is developed for balanced multivariate longitudinal data with known eigenfunctions; second, the CKMM is used to fit unbalanced data where trajectories are aligned on the time axis, and eigenfunctions are unknown; and lastly, a dynamic CKMM (DCKMM) is applied to unbalanced data where trajectories are misaligned, and eigenfunctions are unknown. Expectation-maximization type algorithms are used for parameter estimation. The performance of CKMM is demonstrated on both simulated and real data. / Thesis / Candidate in Philosophy
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/30410 |
| Date | January 2024 |
| Creators | Zhang, Xi |
| Contributors | McNicholas, Paul, Murphy, Orla, Mathematics and Statistics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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