ARAN - Access to Research at NUI Galway

Derivative Estimation in Noisy Data; an Additive Penalty P-Spline Approach

ARAN - Access to Research at NUI Galway

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dc.contributor.advisor Newell, John en
dc.contributor.author Simpkin, Andrew en
dc.date.accessioned 2011-06-14T11:37:09Z en
dc.date.available 2011-06-14T11:37:09Z en
dc.date.issued 2010-12-20 en
dc.identifier.uri http://hdl.handle.net/10379/2002 en
dc.description.abstract In 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.subject Derivative Estimation en
dc.subject P-Splines en
dc.subject Additive Penalty en
dc.subject Smoothing en
dc.title Derivative Estimation in Noisy Data; an Additive Penalty P-Spline Approach en
dc.type Thesis en
dc.contributor.funder IRCSET en
dc.local.note Many 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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