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Estimating the smoothing parameter in generalized spline-based regression

I Cross-validatory criteria for binary data using small sample sizes

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Summary

Estimation of a smooth predictor function in logistic regression requires the determination of a smoothing parameter. Several cross-validatory criteria for finding such a smoothing parameter have been proposed generalizing techniques that are asymptotically well performing for Gaussian data. Here it is argued that a smoothing parameter is a model parameter and can be estimated cross-validating model fit criteria for generalized regression models taking explicitly into account the non-Gaussian distribution of the observed variables. Several criteria based on model choice for binary data are introduced and their performance is investigated in a simulation study where smooth predictor functions are estimated by smoothing splines. The empirical results indicate that cross-validated model fit criteria perform well.

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Acknowledgements

The programs for evaluating the results of smoothing were provided by Elmar Plischke using GAUSS. This study was part of a project on smooth risk functions in 1:1-matched case-control studies and thus integrated within a cooperation with G. Osius. It was granted by the German National Science Foundation (DGF), grant OS-144/1.

The author thanks the referees for very carefully reading the paper and detailed comments that considerably helped to improve the first draft.

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  1. Angelika van der Linde

    Present address: Department of Mathematics and Statistics, University of Edinburgh, Edinburgh, Scotland

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  1. Institute of Statistics, University of Bremen, Bremen, Germany

    Angelika van der Linde

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van der Linde, A. Estimating the smoothing parameter in generalized spline-based regression. Computational Statistics 16, 43–71 (2001). https://doi.org/10.1007/s001800100051

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