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Degrees-of-freedom tests for smoothing splines. (English) Zbl 1019.62038

Summary: 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.

MSC:

62G08 Nonparametric regression and quantile regression
62H15 Hypothesis testing in multivariate analysis
62J05 Linear regression; mixed models

Software:

gamsel
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