Genetic algorithms for the selection of smoothing parameters in additive models |
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Authors: | Rüdiger Krause Gerhard Tutz |
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Institution: | (1) Department of Statistics, Ludwig-Maximilians University, Akademiestr. 1, 80799 München, Germany |
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Abstract: | Summary Additive models of the type y=f
1(x
1)+...+f
p(x
p)+ε where f
j
, j=1,..,p, have unspecified functional form, are flexible statistical regression models which can be used to characterize nonlinear
regression effects. One way of fitting additive models is the expansion in B-splines combined with penalization which prevents
overfitting. The performance of this penalized B-spline (called P-spline) approach strongly depends on the choice of the amount
of smoothing used for components f
j
. In particular for higher dimensional settings this is a computationaly demanding task. In this paper we treat the problem
of choosing the smoothing parameters for P-splines by genetic algorithms. In several simulation studies this approach is compared
to various alternative methods of fitting additive models. In particular functions with different spatial variability are
considered and the effect of constant respectively local adaptive smoothing parameters is evaluated. |
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Keywords: | Additive model Genetic algorithm Penalized regression splines B-splines Improved AIC criterion |
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