Simultaneous selection of variables and smoothing parameters by genetic algorithms

In additive models the problem of variable selection is strongly linked to the choice of the amount of smoothing used for components that represent metrical variables. Many software packages use separate toolsto solve the different tasks of variable selection and smoothing parameter choice. The combinationof these tools often leads to inappropriate results. In this paper we propose a simulataneous choice of variables and smoothing parameters based on genetic algorithms. Common genetic algorithms have to be modified since inclusion of variables and smoothing have to be coded separately but are linked in the search for optimal solutions. The basic tool for fitting the additive model is the penalized expansion in B-splines.