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Please use this identifier to cite or link to this item: http://hdl.handle.net/1974/1575

Title: Multitaper Higher-Order Spectral Analysis of Nonlinear Multivariate Random Processes
Authors: He, HUIXIA

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He_Huixia_200810_PhD.pdfThesis3.46 MBAdobe PDFView/Open
He_Huixia_200810_PhD_EEG_Activation.avisupplmentary video clip (EEG_Activation)151.88 MBAVIView/Open
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 Graduate Theses and Dissertations
Department of Mathematics and Statistics Graduate Theses

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