  In astrophysical (inverse) regression problems it is an important task to
decide whether a given parametric model describes the observational data
sufficiently well or whether a non-parametric modelling becomes necessary.
However, in contrast to common practice this cannot be decided by solely
comparing the quality of fit due to possible over-fitting by the non-parametric
method. Therefore, in this paper we present a resampling algorithm which allows
to decide whether deviations between a parametric and a non-parametric model
are systematic or due to noise. The algorithm is based on a statistical
comparison of the corresponding residuals, under the assumption of the
parametric model as well as under violation of this assumption. This yields a
graphical tool for a robust decision making of parametric versus non-parametric
modelling.
  Moreover, our approach can be used for the selection of the most proper model
among several competitors (model selection). The methods are illustrated by the
problem of recovering the luminosity density in the Milky Way [MW] from
near-infrared [NIR] surface brightness data of the DIRBE experiment on board of
the COBE satellite. Among the parametric models investigated one with 4-armed
spiral structure performs best. In this model the Sagittarius-Carina arm and
its counter-arm are significantly weaker than the other pair of arms.
Furthermore, we find statistical evidence for an improvement over a range of
parametric models with different spiral structure morphologies by a
non-parametric model of Bissantz & Gerhard (2002).
