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Degrees-of-freedom tests for smoothing splines

Hastie, Trevor
Published in Biometrika. 2002, vol. 89, no. 2, p. 251-263
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 modelDegrees of freedom testSmoothing parameter selectionSmoothing spline
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CANTONI, Eva, HASTIE, Trevor. Degrees-of-freedom tests for smoothing splines. In: Biometrika, 2002, vol. 89, n° 2, p. 251-263. https://archive-ouverte.unige.ch/unige:22898

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Deposited on : 2012-09-12

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