Costa, M. J. (2008) Penalized spline models and applications. PhD thesis, University of Warwick.

Preview	Text WRAP_THESIS_Costa_2008.pdf - Submitted Version Download (2864Kb) | Preview
	Other (Permission e-mail) FW digital copy of thesis.msg Restricted to Repository staff only Download (2869Kb)

Abstract

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 manipulate analytically. 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
Date:	July 2008
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Shaw, Ewart
Sponsors:	Fundação para a Ciência e a Tecnologia
Extent:	xvii, 168 leaves : ill., charts
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/3654

Request changes to a record

Actions (login required)

View Item