Within this thesis we consider locally stationary wavelet process models for one and two dimensional data. Unlike the traditional stationary Fourier models this locally stationary wavelet framework allows the second order structure to vary as a function of time (one dimension) or location (two dimensions). We consider three distinct problems within this broader setting. First of all we consider the impact upon one dimensional spectral estimates of the choice of analysing wavelet. As a result of the definition of a locally stationary wavelet process it is required that the same wavelet is used for analysis as generated the process. We show the impact that using an alternative wavelet has on the spectral estimates, showing that, depending on whether the analysing wavelet is smoother than the generating wavelet or not, the spectrum will be under or over estimated. The second problem relates to replicated data. In circumstances where we have data from a number of subjects relating to the same process we may be more interested in the population effects rather than individual subjects. We consider the extension of a mixed effects model to model the spectral structure of replicated locally stationary wavelet processes in order to estimate the population second order structure. Finally we consider the impact of aliasing on locally stationary images. We consider how subsampling an image can lead to artefacts in the spectral structure of the image. By taking advantage of the nature of the contamination in locally stationary two dimensional wavelet processes we show how the artefact may be estimated and a test for the absence of aliasing may be developed.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:658586 |
| Date | January 2013 |
| Creators | Gott, Aimee Nicole |
| Publisher | Lancaster University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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