Journal Article

Soap film smoothing

Wood, Simon N., Bravington, Mark V., Hedley, Sharon L.

2008

Overview

Conventional smoothing methods sometimes perform badly when used to smooth data over complex domains, by smoothing inappropriately across boundary features, such as peninsulas. Solutions to this smoothing problem tend to be computationally complex, and not to provide model smooth functions which are appropriate for incorporating as components of other models, such as generalized additive models or mixed additive models. We propose a class of smoothers that are appropriate for smoothing over difficult regions of [graphic removed] ² which can be represented in terms of a low rank basis and one or two quadratic penalties. The key features of these smoothers are that they do not 'smooth across' boundary features, that their representation in terms of a basis and penalties allows straightforward incorporation as components of generalized additive models, mixed models and other non-standard models, that smoothness selection for these model components is straightforward to accomplish in a computationally efficient manner via generalized cross-validation, Akaike's information criterion or restricted maximum likelihood, for example, and that their low rank means that their use is computationally efficient.

• Publisher: Oxford, UK : Blackwell Publishing Ltd,Blackwell Publishing Ltd,Blackwell Publishing,Blackwell,Royal Statistical Society,Oxford University Press
• Subject: Additives / Antarctic region / Appropriateness / Approximation / Basis / Basis penalty smooth / Boundary conditions / Chlorophylls / Complexity / Components / Criteria / Data analysis / Data smoothing / Differential equation smoothing / Eggs / equations / Exact sciences and technology / FELSPLINE / Fines & penalties / Finite window smoothing / Function values / Functions of a complex variable / General topics / Known boundary smoothing / Mass media images / Mathematical analysis / Mathematical functions / Mathematics / Multivariate analysis / oceans / Owls / Parametric inference / Partial differential equations / Penalties / Peninsulas / Probability and statistics / Probability theory / Regions / Sciences and techniques of general use / Smoothing / Soap / Soaps / Spline / Statistical methods / Statistics / Studies / Validity