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Leitenstorfer, Florian
Tutz, Gerhard
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Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 481
A novel concept for estimating smooth functions by selection techniques based on boosting is developed. It is suggested to put radial basis functions with different spreads at each knot and to do selection and estimation simultaneously by a componentwise boosting algorithm. The methodology of various other smoothing and knot selection procedures (e.g. stepwise selection) is summarized. They are com- pared to the proposed approach by extensive simulations for various unidimensional settings, including varying spatial variation and heteroskedasticity, as well as on a real world data example. Finally, an extension of the proposed method to surface fitting is evaluated numerically on both, simulation and real data. The proposed knot selection technique is shown to be a strong competitor to existing methods for knot selection. - Nonparametric regression ; Knot selection ; Radial basis functions ; Boosting ; Surface fitting
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