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http://hdl.handle.net/1974/1575
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| Title: | Multitaper Higher-Order Spectral Analysis of Nonlinear Multivariate Random Processes |
| Authors: | He, HUIXIA |
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| Keywords: | Canonical Bicoherence (CBC), Canonical Biphase (CBP), Quadratic Phase Coupling (QPC), Multitaper Methods (MTM), Weighted Jackknife, Geomagnetic Field, Solar p-modes, EEG, Nonlinear Multivariate Random Process |
| Issue Date: | 2008 |
| Series/Report no.: | Canadian theses |
| Abstract: | In this work, I will describe a new statistical tool: the canonical bicoherence, which is a combination of the canonical coherence and the bicoherence. I will provide its definitions, properties, estimation by multitaper methods and statistics, and estimate the variance of the estimates by the weighted jackknife method. I will discuss its applicability and usefulness in nonlinear quadratic phase coupling detection and analysis for multivariate random processes. Furthermore, I will develop the time-varying canonical bicoherence for the nonlinear analysis of non-stationary random processes. In this thesis, the canonical bicoherence is mainly applied in two types of data: a) three-component geomagnetic field data, and b) high-dimensional brain electroencephalogram data. Both results obtained will be linked with physical or physiological interpretations. In particular, this thesis is the first work where the novel method of ``canonical bicoherence'' is introduced and applied to the nonlinear quadratic phase coupling detection and analysis for multivariate random processes. |
| Description: | Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2008-10-31 15:03:57.596 |
| URI: | http://hdl.handle.net/1974/1575 |
| Appears in Collections: | Queen's Theses & Dissertations
Mathematics & Statistics Graduate Theses
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