Penalized spline models and applications
Costa, Maria J. (Maria João) (2008) Penalized spline models and applications. PhD thesis, University of Warwick.
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Penalized spline regression models are a popular statistical tool for curve fitting
problems due to their flexibility and computational efficiency. In particular, penalized
cubic spline functions have received a great deal of attention. Cubic splines
have good numerical properties and have proven extremely useful in a variety of
applications. Typically, splines are represented as linear combinations of basis functions.
However, such representations can lack numerical stability or be difficult to
The current thesis proposes a different parametrization for cubic spline functions
that is intuitive and simple to implement. Moreover, integral based penalty
functionals have simple interpretable expressions in terms of the components of the
parametrization. Also, the curvature of the function is not constrained to be continuous
everywhere on its domain, which adds flexibility to the fitting process.
We consider not only models where smoothness is imposed by means of a single
penalty functional, but also a generalization where a combination of different measures
of roughness is built in order to specify the adequate limit of shrinkage for the
problem at hand.
The proposed methodology is illustrated in two distinct regression settings.
|Item Type:||Thesis or Dissertation (PhD)|
|Subjects:||Q Science > QA Mathematics|
|Library of Congress Subject Headings (LCSH):||Curve fitting, Spline theory, Regression analysis -- Mathematical models|
|Official Date:||July 2008|
|Institution:||University of Warwick|
|Theses Department:||Department of Statistics|
|Sponsors:||Fundação para a Ciência e a Tecnologia|
|Extent:||xvii, 168 leaves : ill., charts|
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