en
Scientific article
Open access
English

Degrees-of-freedom tests for smoothing splines

Published inBiometrika, vol. 89, no. 2, p. 251-263
Publication date2002
Abstract

When using smoothing splines to estimate a function, the user faces the problem of choosing the smoothing parameter. Several techniques are available for selecting this parameter according to certain optimality criteria. Here, we take a different point of view and we propose a technique for choosing between two alternatives, for example allowing for two different levels of degrees of freedom. The problem is addressed in the framework of a mixed‐effects model, whose assumptions ensure that the resulting estimator is unbiased. A likelihood‐ratio‐type test statistic is proposed, and its exact distribution is derived. Tests of linearity and overall effect follow directly. We then extend this idea to additive models where it provides a more attractive alternative than multi‐parameter optimisation, and where it gives exact distributional results that can be used in an analysis‐of‐deviance‐type approach. Examples on real data and a simulation study of level and power complete the paper.

Keywords
  • Additive model
  • Degrees of freedom test
  • Smoothing parameter selection
  • Smoothing spline
Citation (ISO format)
CANTONI, Eva, HASTIE, Trevor. Degrees-of-freedom tests for smoothing splines. In: Biometrika, 2002, vol. 89, n° 2, p. 251–263. doi: 10.1093/biomet/89.2.251
Main files (1)
Article (Accepted version)
accessLevelPublic
Identifiers
ISSN of the journal0006-3444
817views
722downloads

Technical informations

Creation09/07/2012 10:55:00 AM
First validation09/07/2012 10:55:00 AM
Update time03/14/2023 5:40:48 PM
Status update03/14/2023 5:40:47 PM
Last indexation05/02/2024 12:39:01 PM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack