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Overview of Redundancy Analysis and Partial Linear Squares and Their Extension to the Frequency Domain

dc.contributor.authorLiu, Jinyi Jr
dc.contributor.copyright-releaseNot Applicableen_US
dc.contributor.degreeMaster of Scienceen_US
dc.contributor.departmentDepartment of Mathematics & Statistics - Statistics Divisionen_US
dc.contributor.ethics-approvalNot Applicableen_US
dc.contributor.external-examinernoneen_US
dc.contributor.graduate-coordinatorDr. Bruce Smithen_US
dc.contributor.manuscriptsNot Applicableen_US
dc.contributor.thesis-readerDr. Bruce Smithen_US
dc.contributor.thesis-readerDr. Michael Dowden_US
dc.contributor.thesis-supervisorDr. Keith R. Thompsonen_US
dc.date.accessioned2011-04-08T16:14:38Z
dc.date.available2011-04-08T16:14:38Z
dc.date.defence2011-04-30
dc.date.issued2011-04-08
dc.description.abstractApplied statisticians are often faced with the problem of dealing with high dimensional data sets when attempting to describe the variability of a single set of variables, or trying to predict the variation of one set of variables from another. In this study, two data reduction methods are described: Redundancy Analysis and Partial Least Squares. A hybrid approach developed by Bougeard et al., (2007) and called Continuum Redundancy-Partial Least Squares, is described. All three methods are extended to the frequency domain in order to allow the lower dimensional subspace used to describe the variability to change with frequency. To illustrate and compare the three methods, and their frequency dependent generalizations, an idealized coupled atmosphere-ocean model is introduced in state space form. This model provides explicit expressions for the covariance and cross spectral matrices required by the various methods; this allows the strengths and weaknesses of the methods to be identified.en_US
dc.identifier.urihttp://hdl.handle.net/10222/13331
dc.language.isoenen_US
dc.subjectAtmosphere-Ocean coupling modelen_US
dc.subjectContinuum Redundancy-Partial Least Squaresen_US
dc.subjectdimension reduction methodsen_US
dc.subjectfrequency domainen_US
dc.subjectmultivariate analysisen_US
dc.subjectPartial Least Squaresen_US
dc.subjectRedundancy Analysisen_US
dc.titleOverview of Redundancy Analysis and Partial Linear Squares and Their Extension to the Frequency Domainen_US

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