| 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. |
