Scientific article
Open access

Degrees-of-freedom tests for smoothing splines

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

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.

  • 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
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Article (Accepted version)
ISSN of the journal0006-3444

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