Multitaper Higher-Order Spectral Analysis of Nonlinear Multivariate Random Processes
Loading...
Authors
He, Huixia
Date
2008-11-04T14:57:03Z
Type
thesis
Language
eng
Keyword
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
Alternative Title
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
Citation
Publisher
License
This 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.