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dc.contributor.advisorNewell, Johnen
dc.contributor.authorSimpkin, Andrewen
dc.date.accessioned2011-06-14T11:37:09Zen
dc.date.available2011-06-14T11:37:09Zen
dc.date.issued2010-12-20en
dc.identifier.urihttp://hdl.handle.net/10379/2002en
dc.description.abstractIn many situations it is of primary interest to estimate the rate of change of the relationship between response and explanatory variables. In this thesis derivative estimation using spline smoothing is explored. A review of derivative estimates found as a by product of several popular spline smoothing techniques is provided. Concerns with these estimates are raised and an additive penalty method utilising the attractive properties of P-Splines is introduced. This approach is shown to improve on semiparametric and P-Spline derivative estimates in simulated smoothing scenarios. Variability bands for derivative estimates are developed for the additive penalty and P-Spline methods with these tested for coverage and precision in further simulations. Motivating examples in environmental, biomedical and astronomical applications are revisited throughout the thesis.en
dc.subjectDerivative Estimationen
dc.subjectP-Splinesen
dc.subjectAdditive Penaltyen
dc.subjectSmoothingen
dc.titleDerivative Estimation in Noisy Data; an Additive Penalty P-Spline Approachen
dc.typeThesisen
dc.contributor.funderIRCSETen
dc.local.noteMany statistical problems with non-linear relationships focus on change and involve derivative estimation and inference. This work proposes an approach based on modified penalised P-spline smoothing incorporating an additive penalty. Applications are made to continuous and count data, including contamination levels in the Irish Sea and annual bird species numbers.en
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