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Multitaper Higher-Order Spectral Analysis of Nonlinear Multivariate Random Processes

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. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2008-10-31 15:03:57.596

Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OKQ.1974/1575
Date04 November 2008
CreatorsHe, HUIXIA
ContributorsQueen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
LanguageEnglish, English
Detected LanguageEnglish
TypeThesis
Format3538548 bytes, application/pdf
RightsThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
RelationCanadian theses

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