Additive Modelling with Penalized Regression Splines and Genetic Algorithms

Additive models of the type y=f_1(x_1)+...+f_p(x_p)+e where
f_j,j=1,...,p, have unspecified functional form, are flexible
statistical regression models which can be used to characterize
nonlinear regression effects. The basic tools used for fitting the
additive model are the expansion in B-splines and penalization
which prevents the problem of overfitting. This penalized B-spline
(called P-spline) approach strongly depends on the choice of the
amount of smoothing used for components f_j. In this paper we treat
the problem of choosing the smoothing parameters by genetic
algorithms. In several simulation studies our approach of
automatically calculation of the smoothing parameters is compared
to alternative methods given in literature. In particular functions
with different spatial variability are considered and the effect of
constant respectively local adaptive smoothing parameters is
evaluated.