Abstract

Independent component analysis (ICA) is wildly used in differently areas. As traditional ICA models make no assumptions on time pattern, they do not take time domain information into consideration. In this thesis, we introduced new assumptions that allow local dependence over time, and we built smooth ICA models to utilize the smoothness information for sources signals. Based on the local dependence assumptions, constrained optimization problems with smoothing penalty were discussed. Then we introduced smooth ICA estimators and estimating equations. Under local dependence assumptions, we gave proofs about the consistency and asymptotic normality of these estimators. We derived the Newton iterative update to solve for smooth ICA estimators, and formulated the complete smooth ICA algorithms in details. The performance on Monte Carlo simulations and implementation on real fMRI datasets were also discussed.

Committee Chair

Jimin Ding

Committee Members

Likai Chen, Jose E. Figueroa-Lopez, Nan Lin, Chengjie Xiong,

Degree

Doctor of Philosophy (PhD)

Author's Department

Mathematics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

Summer 8-15-2021

Language

English (en)

Author's ORCID

http://orcid.org/0000-0002-6597-1591

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Mathematics Commons

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