P-splines regression smoothing and difference type of penalty |
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Authors: | I Gijbels A Verhasselt |
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Institution: | 1.Department of Mathematics and Leuven Statistics Research Center (LStat),Katholieke Universiteit Leuven,Leuven (Heverlee),Belgium |
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Abstract: | P-splines regression provides a flexible smoothing tool. In this paper we consider difference type penalties in a context
of nonparametric generalized linear models, and investigate the impact of the order of the differencing operator. Minimizing
Akaike’s information criterion we search for a possible best data-driven value of the differencing order. Theoretical derivations
are established for the normal model and provide insights into a possible ‘optimal’ choice of the differencing order and its
interrelation with other parameters. Applications of the selection procedure to non-normal models, such as Poisson models,
are given. Simulation studies investigate the performance of the selection procedure and we illustrate its use on real data
examples. |
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